---
_id: '14888'
abstract:
- lang: eng
text: 'A face in a curve arrangement is called popular if it is bounded by the same
curve multiple times. Motivated by the automatic generation of curved nonogram
puzzles, we investigate possibilities to eliminate the popular faces in an arrangement
by inserting a single additional curve. This turns out to be NP-hard; however,
it becomes tractable when the number of popular faces is small: We present a probabilistic
FPT-approach in the number of popular faces.'
acknowledgement: 'This work was initiated at the 16th European Research Week on Geometric
Graphs in Strobl in 2019. A.W. is supported by the Austrian Science Fund (FWF):
W1230. S.T. has been funded by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035].
A preliminary version of this work has been presented at the 38th European Workshop
on Computational Geometry (EuroCG 2022) in Perugia [9]. A full version of this paper,
which includes appendices but is otherwise identical, is available as a technical
report [10].'
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Phoebe
full_name: De Nooijer, Phoebe
last_name: De Nooijer
- first_name: Soeren
full_name: Terziadis, Soeren
last_name: Terziadis
- first_name: Alexandra
full_name: Weinberger, Alexandra
last_name: Weinberger
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tamara
full_name: Mchedlidze, Tamara
last_name: Mchedlidze
- first_name: Maarten
full_name: Löffler, Maarten
last_name: Löffler
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
citation:
ama: 'De Nooijer P, Terziadis S, Weinberger A, et al. Removing popular faces in curve
arrangements. In: 31st International Symposium on Graph Drawing and Network
Visualization. Vol 14466. Springer Nature; 2024:18-33. doi:10.1007/978-3-031-49275-4_2'
apa: 'De Nooijer, P., Terziadis, S., Weinberger, A., Masárová, Z., Mchedlidze, T.,
Löffler, M., & Rote, G. (2024). Removing popular faces in curve arrangements.
In 31st International Symposium on Graph Drawing and Network Visualization
(Vol. 14466, pp. 18–33). Isola delle Femmine, Palermo, Italy: Springer Nature.
https://doi.org/10.1007/978-3-031-49275-4_2'
chicago: De Nooijer, Phoebe, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová,
Tamara Mchedlidze, Maarten Löffler, and Günter Rote. “Removing Popular Faces in Curve
Arrangements.” In 31st International Symposium on Graph Drawing and Network
Visualization, 14466:18–33. Springer Nature, 2024. https://doi.org/10.1007/978-3-031-49275-4_2.
ieee: P. De Nooijer et al., “Removing popular faces in curve arrangements,”
in 31st International Symposium on Graph Drawing and Network Visualization,
Isola delle Femmine, Palermo, Italy, 2024, vol. 14466, pp. 18–33.
ista: 'De Nooijer P, Terziadis S, Weinberger A, Masárová Z, Mchedlidze T, Löffler
M, Rote G. 2024. Removing popular faces in curve arrangements. 31st International
Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network
Visualization, LNCS, vol. 14466, 18–33.'
mla: De Nooijer, Phoebe, et al. “Removing Popular Faces in Curve Arrangements.”
31st International Symposium on Graph Drawing and Network Visualization,
vol. 14466, Springer Nature, 2024, pp. 18–33, doi:10.1007/978-3-031-49275-4_2.
short: P. De Nooijer, S. Terziadis, A. Weinberger, Z. Masárová, T. Mchedlidze, M.
Löffler, G. Rote, in:, 31st International Symposium on Graph Drawing and Network
Visualization, Springer Nature, 2024, pp. 18–33.
conference:
end_date: 2023-09-22
location: Isola delle Femmine, Palermo, Italy
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2023-09-20
date_created: 2024-01-28T23:01:43Z
date_published: 2024-01-06T00:00:00Z
date_updated: 2025-07-21T07:28:03Z
day: '06'
department:
- _id: UlWa
- _id: HeEd
doi: 10.1007/978-3-031-49275-4_2
external_id:
arxiv:
- '2202.12175'
intvolume: ' 14466'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2202.12175
month: '01'
oa: 1
oa_version: Preprint
page: 18-33
project:
- _id: bdb2a702-d553-11ed-ba76-f12e3e5a3bc6
grant_number: '101087907'
name: 'A quantum hybrid of atoms and milligram-scale pendulums: towards gravitational
quantum mechanics'
publication: 31st International Symposium on Graph Drawing and Network Visualization
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783031492747'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Removing popular faces in curve arrangements
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14466
year: '2024'
...
---
_id: '14445'
abstract:
- lang: eng
text: "We prove the following quantitative Borsuk–Ulam-type result (an equivariant
analogue of Gromov’s Topological Overlap Theorem): Let X be a free ℤ/2-complex
of dimension d with coboundary expansion at least ηk in dimension 0 ≤ k < d. Then
for every equivariant map F: X →ℤ/2 ℝd, the fraction of d-simplices σ of X with
0 ∈ F (σ) is at least 2−d Π d−1k=0ηk.\r\n\r\nAs an application, we show that for
every sufficiently thick d-dimensional spherical building Y and every map f: Y
→ ℝ2d, we have f(σ) ∩ f(τ) ≠ ∅ for a constant fraction μd > 0 of pairs {σ, τ}
of d-simplices of Y. In particular, such complexes are non-embeddable into ℝ2d,
which proves a conjecture of Tancer and Vorwerk for sufficiently thick spherical
buildings.\r\n\r\nWe complement these results by upper bounds on the coboundary
expansion of two families of simplicial complexes; this indicates some limitations
to the bounds one can obtain by straighforward applications of the quantitative
Borsuk–Ulam theorem. Specifically, we prove\r\n\r\n• an upper bound of (d + 1)/2d
on the normalized (d − 1)-th coboundary expansion constant of complete (d + 1)-partite
d-dimensional complexes (under a mild divisibility assumption on the sizes of
the parts); and\r\n\r\n• an upper bound of (d + 1)/2d + ε on the normalized (d
− 1)-th coboundary expansion of the d-dimensional spherical building associated
with GLd+2(Fq) for any ε > 0 and sufficiently large q. This disproves, in a rather
strong sense, a conjecture of Lubotzky, Meshulam and Mozes."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
- first_name: Pascal
full_name: Wild, Pascal
id: 4C20D868-F248-11E8-B48F-1D18A9856A87
last_name: Wild
citation:
ama: Wagner U, Wild P. Coboundary expansion, equivariant overlap, and crossing numbers
of simplicial complexes. Israel Journal of Mathematics. 2023;256(2):675-717.
doi:10.1007/s11856-023-2521-9
apa: Wagner, U., & Wild, P. (2023). Coboundary expansion, equivariant overlap,
and crossing numbers of simplicial complexes. Israel Journal of Mathematics.
Springer Nature. https://doi.org/10.1007/s11856-023-2521-9
chicago: Wagner, Uli, and Pascal Wild. “Coboundary Expansion, Equivariant Overlap,
and Crossing Numbers of Simplicial Complexes.” Israel Journal of Mathematics.
Springer Nature, 2023. https://doi.org/10.1007/s11856-023-2521-9.
ieee: U. Wagner and P. Wild, “Coboundary expansion, equivariant overlap, and crossing
numbers of simplicial complexes,” Israel Journal of Mathematics, vol. 256,
no. 2. Springer Nature, pp. 675–717, 2023.
ista: Wagner U, Wild P. 2023. Coboundary expansion, equivariant overlap, and crossing
numbers of simplicial complexes. Israel Journal of Mathematics. 256(2), 675–717.
mla: Wagner, Uli, and Pascal Wild. “Coboundary Expansion, Equivariant Overlap, and
Crossing Numbers of Simplicial Complexes.” Israel Journal of Mathematics,
vol. 256, no. 2, Springer Nature, 2023, pp. 675–717, doi:10.1007/s11856-023-2521-9.
short: U. Wagner, P. Wild, Israel Journal of Mathematics 256 (2023) 675–717.
date_created: 2023-10-22T22:01:14Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2023-12-13T13:09:07Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s11856-023-2521-9
external_id:
isi:
- '001081646400010'
file:
- access_level: open_access
checksum: fbb05619fe4b650f341cc730425dd9c3
content_type: application/pdf
creator: dernst
date_created: 2023-10-31T11:20:31Z
date_updated: 2023-10-31T11:20:31Z
file_id: '14475'
file_name: 2023_IsraelJourMath_Wagner.pdf
file_size: 623787
relation: main_file
success: 1
file_date_updated: 2023-10-31T11:20:31Z
has_accepted_license: '1'
intvolume: ' 256'
isi: 1
issue: '2'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 675-717
publication: Israel Journal of Mathematics
publication_identifier:
eissn:
- 1565-8511
issn:
- 0021-2172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Coboundary expansion, equivariant overlap, and crossing numbers of simplicial
complexes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 256
year: '2023'
...
---
_id: '14660'
abstract:
- lang: eng
text: "The classical Steinitz theorem states that if the origin belongs to the interior
of the convex hull of a set \U0001D446⊂ℝ\U0001D451, then there are at most 2\U0001D451
points of \U0001D446 whose convex hull contains the origin in the interior. Bárány,
Katchalski,and Pach proved the following quantitative version of Steinitz’s theorem.
Let \U0001D444 be a convex polytope in ℝ\U0001D451 containing the standard Euclidean
unit ball \U0001D401\U0001D451. Then there exist at most 2\U0001D451 vertices
of \U0001D444 whose convex hull \U0001D444′ satisfies \U0001D45F\U0001D401\U0001D451⊂\U0001D444′
with \U0001D45F⩾\U0001D451−2\U0001D451. They conjectured that \U0001D45F⩾\U0001D450\U0001D451−1∕2
holds with a universal constant \U0001D450>0. We prove \U0001D45F⩾15\U0001D4512,
the first polynomial lower bound on \U0001D45F. Furthermore, we show that \U0001D45F
is not greater than 2/√\U0001D451."
acknowledgement: M.N. was supported by the János Bolyai Scholarship of the Hungarian
Academy of Sciences aswell as the National Research, Development and Innovation
Fund (NRDI) grants K119670 andK131529, and the ÚNKP-22-5 New National Excellence
Program of the Ministry for Innovationand Technology from the source of the NRDI
as well as the ELTE TKP 2021-NKTA-62 fundingscheme
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
- first_name: Márton
full_name: Naszódi, Márton
last_name: Naszódi
citation:
ama: 'Ivanov G, Naszódi M. Quantitative Steinitz theorem: A polynomial bound. Bulletin
of the London Mathematical Society. 2023. doi:10.1112/blms.12965'
apa: 'Ivanov, G., & Naszódi, M. (2023). Quantitative Steinitz theorem: A polynomial
bound. Bulletin of the London Mathematical Society. London Mathematical
Society. https://doi.org/10.1112/blms.12965'
chicago: 'Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A
Polynomial Bound.” Bulletin of the London Mathematical Society. London
Mathematical Society, 2023. https://doi.org/10.1112/blms.12965.'
ieee: 'G. Ivanov and M. Naszódi, “Quantitative Steinitz theorem: A polynomial bound,”
Bulletin of the London Mathematical Society. London Mathematical Society,
2023.'
ista: 'Ivanov G, Naszódi M. 2023. Quantitative Steinitz theorem: A polynomial bound.
Bulletin of the London Mathematical Society.'
mla: 'Ivanov, Grigory, and Márton Naszódi. “Quantitative Steinitz Theorem: A Polynomial
Bound.” Bulletin of the London Mathematical Society, London Mathematical
Society, 2023, doi:10.1112/blms.12965.'
short: G. Ivanov, M. Naszódi, Bulletin of the London Mathematical Society (2023).
date_created: 2023-12-10T23:00:58Z
date_published: 2023-12-04T00:00:00Z
date_updated: 2023-12-11T10:03:54Z
day: '04'
department:
- _id: UlWa
doi: 10.1112/blms.12965
external_id:
arxiv:
- '2212.04308'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.1112/blms.12965'
month: '12'
oa: 1
oa_version: Published Version
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- 1469-2120
issn:
- 0024-6093
publication_status: epub_ahead
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Quantitative Steinitz theorem: A polynomial bound'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14737'
abstract:
- lang: eng
text: 'John’s fundamental theorem characterizing the largest volume ellipsoid contained
in a convex body $K$ in $\mathbb{R}^{d}$ has seen several generalizations and
extensions. One direction, initiated by V. Milman is to replace ellipsoids by
positions (affine images) of another body $L$. Another, more recent direction
is to consider logarithmically concave functions on $\mathbb{R}^{d}$ instead of
convex bodies: we designate some special, radially symmetric log-concave function
$g$ as the analogue of the Euclidean ball, and want to find its largest integral
position under the constraint that it is pointwise below some given log-concave
function $f$. We follow both directions simultaneously: we consider the functional
question, and allow essentially any meaningful function to play the role of $g$
above. Our general theorems jointly extend known results in both directions. The
dual problem in the setting of convex bodies asks for the smallest volume ellipsoid,
called Löwner’s ellipsoid, containing $K$. We consider the analogous problem for
functions: we characterize the solutions of the optimization problem of finding
a smallest integral position of some log-concave function $g$ under the constraint
that it is pointwise above $f$. It turns out that in the functional setting, the
relationship between the John and the Löwner problems is more intricate than it
is in the setting of convex bodies.'
acknowledgement: "We thank Alexander Litvak for the many discussions on Theorem 1.1.
Igor Tsiutsiurupa participated in the early stage of this project. To our deep regret,
Igor chose another road for his life and stopped working with us.\r\nThis work was
supported by the János Bolyai Scholarship of the Hungarian Academy of Sciences [to
M.N.]; the National Research, Development, and Innovation Fund (NRDI) [K119670 and
K131529 to M.N.]; and the ÚNKP-22-5 New National Excellence Program of the Ministry
for Innovation and Technology from the source of the NRDI [to M.N.]."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
- first_name: Márton
full_name: Naszódi, Márton
last_name: Naszódi
citation:
ama: Ivanov G, Naszódi M. Functional John and Löwner conditions for pairs of log-concave
functions. International Mathematics Research Notices. 2023;2023(23):20613-20669.
doi:10.1093/imrn/rnad210
apa: Ivanov, G., & Naszódi, M. (2023). Functional John and Löwner conditions
for pairs of log-concave functions. International Mathematics Research Notices.
Oxford University Press. https://doi.org/10.1093/imrn/rnad210
chicago: Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions
for Pairs of Log-Concave Functions.” International Mathematics Research Notices.
Oxford University Press, 2023. https://doi.org/10.1093/imrn/rnad210.
ieee: G. Ivanov and M. Naszódi, “Functional John and Löwner conditions for pairs
of log-concave functions,” International Mathematics Research Notices,
vol. 2023, no. 23. Oxford University Press, pp. 20613–20669, 2023.
ista: Ivanov G, Naszódi M. 2023. Functional John and Löwner conditions for pairs
of log-concave functions. International Mathematics Research Notices. 2023(23),
20613–20669.
mla: Ivanov, Grigory, and Márton Naszódi. “Functional John and Löwner Conditions
for Pairs of Log-Concave Functions.” International Mathematics Research Notices,
vol. 2023, no. 23, Oxford University Press, 2023, pp. 20613–69, doi:10.1093/imrn/rnad210.
short: G. Ivanov, M. Naszódi, International Mathematics Research Notices 2023 (2023)
20613–20669.
date_created: 2024-01-08T09:48:56Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-01-08T09:57:25Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1093/imrn/rnad210
external_id:
arxiv:
- '2212.11781'
file:
- access_level: open_access
checksum: 353666cea80633beb0f1ffd342dff6d4
content_type: application/pdf
creator: dernst
date_created: 2024-01-08T09:53:09Z
date_updated: 2024-01-08T09:53:09Z
file_id: '14738'
file_name: 2023_IMRN_Ivanov.pdf
file_size: 815777
relation: main_file
success: 1
file_date_updated: 2024-01-08T09:53:09Z
has_accepted_license: '1'
intvolume: ' 2023'
issue: '23'
keyword:
- General Mathematics
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 20613-20669
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
status: public
title: Functional John and Löwner conditions for pairs of log-concave functions
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2023
year: '2023'
...
---
_id: '13270'
abstract:
- lang: eng
text: "Consider a geodesic triangle on a surface of constant curvature and subdivide
it recursively into four triangles by joining the midpoints of its edges. We show
the existence of a uniform δ>0\r\n such that, at any step of the subdivision,
all the triangle angles lie in the interval (δ,π−δ)\r\n. Additionally, we exhibit
stabilising behaviours for both angles and lengths as this subdivision progresses."
acknowledgement: Open access funding provided by the Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Florestan R
full_name: Brunck, Florestan R
id: 6ab6e556-f394-11eb-9cf6-9dfb78f00d8d
last_name: Brunck
citation:
ama: Brunck FR. Iterated medial triangle subdivision in surfaces of constant curvature.
Discrete and Computational Geometry. 2023;70(3):1059-1089. doi:10.1007/s00454-023-00500-5
apa: Brunck, F. R. (2023). Iterated medial triangle subdivision in surfaces of constant
curvature. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-023-00500-5
chicago: Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces
of Constant Curvature.” Discrete and Computational Geometry. Springer Nature,
2023. https://doi.org/10.1007/s00454-023-00500-5.
ieee: F. R. Brunck, “Iterated medial triangle subdivision in surfaces of constant
curvature,” Discrete and Computational Geometry, vol. 70, no. 3. Springer
Nature, pp. 1059–1089, 2023.
ista: Brunck FR. 2023. Iterated medial triangle subdivision in surfaces of constant
curvature. Discrete and Computational Geometry. 70(3), 1059–1089.
mla: Brunck, Florestan R. “Iterated Medial Triangle Subdivision in Surfaces of Constant
Curvature.” Discrete and Computational Geometry, vol. 70, no. 3, Springer
Nature, 2023, pp. 1059–89, doi:10.1007/s00454-023-00500-5.
short: F.R. Brunck, Discrete and Computational Geometry 70 (2023) 1059–1089.
date_created: 2023-07-23T22:01:14Z
date_published: 2023-07-05T00:00:00Z
date_updated: 2024-01-29T11:16:16Z
day: '05'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s00454-023-00500-5
external_id:
arxiv:
- '2107.04112'
isi:
- '001023742800003'
file:
- access_level: open_access
checksum: 865e68daafdd4edcfc280172ec50f5ea
content_type: application/pdf
creator: dernst
date_created: 2024-01-29T11:15:22Z
date_updated: 2024-01-29T11:15:22Z
file_id: '14897'
file_name: 2023_DiscreteComputGeometry_Brunck.pdf
file_size: 1466020
relation: main_file
success: 1
file_date_updated: 2024-01-29T11:15:22Z
has_accepted_license: '1'
intvolume: ' 70'
isi: 1
issue: '3'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 1059-1089
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Iterated medial triangle subdivision in surfaces of constant curvature
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 70
year: '2023'
...
---
_id: '13331'
abstract:
- lang: eng
text: "The extension of extremal combinatorics to the setting of exterior algebra
is a work\r\nin progress that gained attention recently. In this thesis, we study
the combinatorial structure of exterior algebra by introducing a dictionary that
translates the notions from the set systems into the framework of exterior algebra.
We show both generalizations of celebrated Erdös--Ko--Rado theorem and Hilton--Milner
theorem to the setting of exterior algebra in the simplest non-trivial case of
two-forms.\r\n"
alternative_title:
- ISTA Master's Thesis
article_processing_charge: No
author:
- first_name: Seyda
full_name: Köse, Seyda
id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb
last_name: Köse
citation:
ama: Köse S. Exterior algebra and combinatorics. 2023. doi:10.15479/at:ista:13331
apa: Köse, S. (2023). Exterior algebra and combinatorics. Institute of Science
and Technology Austria. https://doi.org/10.15479/at:ista:13331
chicago: Köse, Seyda. “Exterior Algebra and Combinatorics.” Institute of Science
and Technology Austria, 2023. https://doi.org/10.15479/at:ista:13331.
ieee: S. Köse, “Exterior algebra and combinatorics,” Institute of Science and Technology
Austria, 2023.
ista: Köse S. 2023. Exterior algebra and combinatorics. Institute of Science and
Technology Austria.
mla: Köse, Seyda. Exterior Algebra and Combinatorics. Institute of Science
and Technology Austria, 2023, doi:10.15479/at:ista:13331.
short: S. Köse, Exterior Algebra and Combinatorics, Institute of Science and Technology
Austria, 2023.
date_created: 2023-07-31T10:20:55Z
date_published: 2023-07-31T00:00:00Z
date_updated: 2023-10-04T11:54:56Z
day: '31'
ddc:
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- '516'
degree_awarded: MS
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- _id: UlWa
doi: 10.15479/at:ista:13331
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- 2791-4585
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
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relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
title: Exterior algebra and combinatorics
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '13969'
abstract:
- lang: eng
text: "Bundling crossings is a strategy which can enhance the readability\r\nof
graph drawings. In this paper we consider good drawings, i.e., we require that\r\nany
two edges have at most one common point which can be a common vertex or a\r\ncrossing.
Our main result is that there is a polynomial-time algorithm to compute an\r\n8-approximation
of the bundled crossing number of a good drawing with no toothed\r\nhole. In general
the number of toothed holes has to be added to the 8-approximation.\r\nIn the
special case of circular drawings the approximation factor is 8, this improves\r\nupon
the 10-approximation of Fink et al. [14]. Our approach also works with the same\r\napproximation
factor for families of pseudosegments, i.e., curves intersecting at most\r\nonce.
We also show how to compute a 9/2-approximation when the intersection graph of\r\nthe
pseudosegments is bipartite and has no toothed hole."
acknowledgement: This work was initiated during the Workshop on Geometric Graphs in
November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian
Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during
the workshop. The first author has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement
No 754411. The second author has been supported by the German Research Foundation
DFG Project FE 340/12-1. An extended abstract of this paper has been published in
the proceedings of WALCOM 2022 in the Springer LNCS series, vol. 13174, pages 383–395.
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Stefan
full_name: Felsner, Stefan
last_name: Felsner
citation:
ama: Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. Journal
of Graph Algorithms and Applications. 2023;27(6):433-457. doi:10.7155/jgaa.00629
apa: Arroyo Guevara, A. M., & Felsner, S. (2023). Approximating the bundled
crossing number. Journal of Graph Algorithms and Applications. Brown University.
https://doi.org/10.7155/jgaa.00629
chicago: Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled
Crossing Number.” Journal of Graph Algorithms and Applications. Brown University,
2023. https://doi.org/10.7155/jgaa.00629.
ieee: A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing number,”
Journal of Graph Algorithms and Applications, vol. 27, no. 6. Brown University,
pp. 433–457, 2023.
ista: Arroyo Guevara AM, Felsner S. 2023. Approximating the bundled crossing number.
Journal of Graph Algorithms and Applications. 27(6), 433–457.
mla: Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing
Number.” Journal of Graph Algorithms and Applications, vol. 27, no. 6,
Brown University, 2023, pp. 433–57, doi:10.7155/jgaa.00629.
short: A.M. Arroyo Guevara, S. Felsner, Journal of Graph Algorithms and Applications
27 (2023) 433–457.
date_created: 2023-08-06T22:01:11Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-09-25T10:56:10Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.7155/jgaa.00629
ec_funded: 1
external_id:
arxiv:
- '2109.14892'
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creator: dernst
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date_updated: 2023-08-07T08:00:48Z
file_id: '13979'
file_name: 2023_JourGraphAlgorithms_Arroyo.pdf
file_size: 865774
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success: 1
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month: '07'
oa: 1
oa_version: Published Version
page: 433-457
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of Graph Algorithms and Applications
publication_identifier:
issn:
- 1526-1719
publication_status: published
publisher: Brown University
quality_controlled: '1'
related_material:
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scopus_import: '1'
status: public
title: Approximating the bundled crossing number
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 27
year: '2023'
...
---
_id: '13974'
abstract:
- lang: eng
text: The Tverberg theorem is one of the cornerstones of discrete geometry. It states
that, given a set X of at least (d+1)(r−1)+1 points in Rd, one can find a partition
X=X1∪⋯∪Xr of X, such that the convex hulls of the Xi, i=1,…,r, all share a common
point. In this paper, we prove a trengthening of this theorem that guarantees
a partition which, in addition to the above, has the property that the boundaries
of full-dimensional convex hulls have pairwise nonempty intersections. Possible
generalizations and algorithmic aspects are also discussed. As a concrete application,
we show that any n points in the plane in general position span ⌊n/3⌋ vertex-disjoint
triangles that are pairwise crossing, meaning that their boundaries have pairwise
nonempty intersections; this number is clearly best possible. A previous result
of Álvarez-Rebollar et al. guarantees ⌊n/6⌋pairwise crossing triangles. Our result
generalizes to a result about simplices in Rd, d≥2.
acknowledgement: "Part of the research leading to this paper was done during the 16th
Gremo Workshop on Open Problems (GWOP), Waltensburg, Switzerland, June 12–16, 2018.
We thank Patrick Schnider for suggesting the problem, and Stefan Felsner, Malte
Milatz, and Emo Welzl for fruitful discussions during the workshop. We also thank
Stefan Felsner and Manfred Scheucher for finding, communicating the example from
Sect. 3.3, and the kind permission to include their visualization of the point set.
We thank Dömötör Pálvölgyi, the SoCG reviewers, and DCG reviewers for various helpful
comments.\r\nR. Fulek gratefully acknowledges support from Austrian Science Fund
(FWF), Project M2281-N35. A. Kupavskii was supported by the Advanced Postdoc.Mobility
Grant no. P300P2_177839 of the Swiss National Science Foundation. Research by P.
Valtr was supported by the Grant no. 18-19158 S of the Czech Science Foundation
(GAČR)."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Radoslav
full_name: Fulek, Radoslav
id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87
last_name: Fulek
orcid: 0000-0001-8485-1774
- first_name: Bernd
full_name: Gärtner, Bernd
last_name: Gärtner
- first_name: Andrey
full_name: Kupavskii, Andrey
last_name: Kupavskii
- first_name: Pavel
full_name: Valtr, Pavel
last_name: Valtr
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. The crossing Tverberg theorem.
Discrete and Computational Geometry. 2023. doi:10.1007/s00454-023-00532-x
apa: Fulek, R., Gärtner, B., Kupavskii, A., Valtr, P., & Wagner, U. (2023).
The crossing Tverberg theorem. Discrete and Computational Geometry. Springer
Nature. https://doi.org/10.1007/s00454-023-00532-x
chicago: Fulek, Radoslav, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli
Wagner. “The Crossing Tverberg Theorem.” Discrete and Computational Geometry.
Springer Nature, 2023. https://doi.org/10.1007/s00454-023-00532-x.
ieee: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing
Tverberg theorem,” Discrete and Computational Geometry. Springer Nature,
2023.
ista: Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2023. The crossing Tverberg
theorem. Discrete and Computational Geometry.
mla: Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” Discrete and Computational
Geometry, Springer Nature, 2023, doi:10.1007/s00454-023-00532-x.
short: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, Discrete and Computational
Geometry (2023).
date_created: 2023-08-06T22:01:12Z
date_published: 2023-07-27T00:00:00Z
date_updated: 2023-12-13T12:03:35Z
day: '27'
department:
- _id: UlWa
doi: 10.1007/s00454-023-00532-x
external_id:
arxiv:
- '1812.04911'
isi:
- '001038546500001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1812.04911
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 261FA626-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02281
name: Eliminating intersections in drawings of graphs
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '6647'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The crossing Tverberg theorem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '9651'
abstract:
- lang: eng
text: We introduce a hierachy of equivalence relations on the set of separated nets
of a given Euclidean space, indexed by concave increasing functions ϕ:(0,∞)→(0,∞).
Two separated nets are called ϕ-displacement equivalent if, roughly speaking,
there is a bijection between them which, for large radii R, displaces points of
norm at most R by something of order at most ϕ(R). We show that the spectrum of
ϕ-displacement equivalence spans from the established notion of bounded displacement
equivalence, which corresponds to bounded ϕ, to the indiscrete equivalence relation,
coresponding to ϕ(R)∈Ω(R), in which all separated nets are equivalent. In between
the two ends of this spectrum, the notions of ϕ-displacement equivalence are shown
to be pairwise distinct with respect to the asymptotic classes of ϕ(R) for R→∞.
We further undertake a comparison of our notion of ϕ-displacement equivalence
with previously studied relations on separated nets. Particular attention is given
to the interaction of the notions of ϕ-displacement equivalence with that of bilipschitz
equivalence.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). This work was started while both authors were employed at the University
of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35.
It was continued when the first named author was employed at University of Leipzig
and the second named author was employed at Institute of Science and Technology
of Austria, where he was supported by an IST Fellowship.'
article_number: '15'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Michael
full_name: Dymond, Michael
last_name: Dymond
- first_name: Vojtech
full_name: Kaluza, Vojtech
id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E
last_name: Kaluza
orcid: 0000-0002-2512-8698
citation:
ama: Dymond M, Kaluza V. Divergence of separated nets with respect to displacement
equivalence. Geometriae Dedicata. 2023. doi:10.1007/s10711-023-00862-3
apa: Dymond, M., & Kaluza, V. (2023). Divergence of separated nets with respect
to displacement equivalence. Geometriae Dedicata. Springer Nature. https://doi.org/10.1007/s10711-023-00862-3
chicago: Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with
Respect to Displacement Equivalence.” Geometriae Dedicata. Springer Nature,
2023. https://doi.org/10.1007/s10711-023-00862-3.
ieee: M. Dymond and V. Kaluza, “Divergence of separated nets with respect to displacement
equivalence,” Geometriae Dedicata. Springer Nature, 2023.
ista: Dymond M, Kaluza V. 2023. Divergence of separated nets with respect to displacement
equivalence. Geometriae Dedicata., 15.
mla: Dymond, Michael, and Vojtech Kaluza. “Divergence of Separated Nets with Respect
to Displacement Equivalence.” Geometriae Dedicata, 15, Springer Nature,
2023, doi:10.1007/s10711-023-00862-3.
short: M. Dymond, V. Kaluza, Geometriae Dedicata (2023).
date_created: 2021-07-14T07:01:27Z
date_published: 2023-11-17T00:00:00Z
date_updated: 2024-01-11T13:06:32Z
day: '17'
department:
- _id: UlWa
doi: 10.1007/s10711-023-00862-3
external_id:
arxiv:
- '2102.13046'
isi:
- '001105681500001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s10711-023-00862-3
month: '11'
oa: 1
oa_version: Published Version
publication: Geometriae Dedicata
publication_identifier:
eissn:
- 1572-9168
issn:
- 0046-5755
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Divergence of separated nets with respect to displacement equivalence
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '9652'
abstract:
- lang: eng
text: In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated
nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice.
We study weaker notions of equivalence of separated nets and demonstrate that
such notions also give rise to distinct equivalence classes. Put differently,
we find occurrences of particularly strong divergence of separated nets from the
integer lattice. Our approach generalises that of Burago and Kleiner and McMullen
which takes place largely in a continuous setting. Existence of irregular separated
nets is verified via the existence of non-realisable density functions ρ:[0,1]d→(0,∞).
In the present work we obtain stronger types of non-realisable densities.
acknowledgement: 'This work was done while both authors were employed at the University
of Innsbruck and enjoyed the full support of Austrian Science Fund (FWF): P 30902-N35.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Michael
full_name: Dymond, Michael
last_name: Dymond
- first_name: Vojtech
full_name: Kaluza, Vojtech
id: 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E
last_name: Kaluza
orcid: 0000-0002-2512-8698
citation:
ama: Dymond M, Kaluza V. Highly irregular separated nets. Israel Journal of Mathematics.
2023;253:501-554. doi:10.1007/s11856-022-2448-6
apa: Dymond, M., & Kaluza, V. (2023). Highly irregular separated nets. Israel
Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s11856-022-2448-6
chicago: Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.”
Israel Journal of Mathematics. Springer Nature, 2023. https://doi.org/10.1007/s11856-022-2448-6.
ieee: M. Dymond and V. Kaluza, “Highly irregular separated nets,” Israel Journal
of Mathematics, vol. 253. Springer Nature, pp. 501–554, 2023.
ista: Dymond M, Kaluza V. 2023. Highly irregular separated nets. Israel Journal
of Mathematics. 253, 501–554.
mla: Dymond, Michael, and Vojtech Kaluza. “Highly Irregular Separated Nets.” Israel
Journal of Mathematics, vol. 253, Springer Nature, 2023, pp. 501–54, doi:10.1007/s11856-022-2448-6.
short: M. Dymond, V. Kaluza, Israel Journal of Mathematics 253 (2023) 501–554.
date_created: 2021-07-14T07:01:28Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2023-08-14T11:26:34Z
day: '01'
ddc:
- '515'
- '516'
department:
- _id: UlWa
doi: 10.1007/s11856-022-2448-6
external_id:
arxiv:
- '1903.05923'
isi:
- '000904950300003'
file:
- access_level: open_access
checksum: 6fa0a3207dd1d6467c309fd1bcc867d1
content_type: application/pdf
creator: vkaluza
date_created: 2021-07-14T07:41:50Z
date_updated: 2021-07-14T07:41:50Z
file_id: '9653'
file_name: separated_nets.pdf
file_size: 900422
relation: main_file
file_date_updated: 2021-07-14T07:41:50Z
has_accepted_license: '1'
intvolume: ' 253'
isi: 1
keyword:
- Lipschitz
- bilipschitz
- bounded displacement
- modulus of continuity
- separated net
- non-realisable density
- Burago--Kleiner construction
language:
- iso: eng
month: '03'
oa: 1
oa_version: Submitted Version
page: 501-554
publication: Israel Journal of Mathematics
publication_identifier:
eissn:
- 1565-8511
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Highly irregular separated nets
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 253
year: '2023'
...
---
_id: '11999'
abstract:
- lang: eng
text: 'A simple drawing D(G) of a graph G is one where each pair of edges share
at most one point: either a common endpoint or a proper crossing. An edge e in
the complement of G can be inserted into D(G) if there exists a simple drawing
of G+e extending D(G). As a result of Levi’s Enlargement Lemma, if a drawing is
rectilinear (pseudolinear), that is, the edges can be extended into an arrangement
of lines (pseudolines), then any edge in the complement of G can be inserted.
In contrast, we show that it is NP-complete to decide whether one edge can be
inserted into a simple drawing. This remains true even if we assume that the drawing
is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles.
On the positive side, we show that, given an arrangement of pseudocircles A and
a pseudosegment σ, it can be decided in polynomial time whether there exists a
pseudocircle Φσ extending σ for which A∪{Φσ} is again an arrangement of pseudocircles.'
acknowledgement: 'This work was started during the 6th Austrian–Japanese–Mexican–Spanish
Workshop on Discrete Geometry in June 2019 in Austria. We thank all the participants
for the good atmosphere as well as discussions on the topic. Also, we thank Jan
Kynčl for sending us remarks on a preliminary version of this work and an anonymous
referee for further helpful comments.Alan Arroyo was funded by the Marie Skłodowska-Curie
grant agreement No 754411. Fabian Klute was partially supported by the Netherlands
Organisation for Scientific Research (NWO) under project no. 612.001.651 and by
the Austrian Science Fund (FWF): J-4510. Irene Parada and Birgit Vogtenhuber were
partially supported by the Austrian Science Fund (FWF): W1230 and within the collaborative
DACH project Arrangements and Drawings as FWF project I 3340-N35. Irene Parada was
also partially supported by the Independent Research Fund Denmark grant 2020-2023
(9131-00044B) Dynamic Network Analysis and by the Margarita Salas Fellowship funded
by the Ministry of Universities of Spain and the European Union (NextGenerationEU).
Tilo Wiedera was supported by the German Research Foundation (DFG) grant CH 897/2-2.'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Fabian
full_name: Klute, Fabian
last_name: Klute
- first_name: Irene
full_name: Parada, Irene
last_name: Parada
- first_name: Birgit
full_name: Vogtenhuber, Birgit
last_name: Vogtenhuber
- first_name: Raimund
full_name: Seidel, Raimund
last_name: Seidel
- first_name: Tilo
full_name: Wiedera, Tilo
last_name: Wiedera
citation:
ama: Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T. Inserting
one edge into a simple drawing is hard. Discrete and Computational Geometry.
2023;69:745–770. doi:10.1007/s00454-022-00394-9
apa: Arroyo Guevara, A. M., Klute, F., Parada, I., Vogtenhuber, B., Seidel, R.,
& Wiedera, T. (2023). Inserting one edge into a simple drawing is hard. Discrete
and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00394-9
chicago: Arroyo Guevara, Alan M, Fabian Klute, Irene Parada, Birgit Vogtenhuber,
Raimund Seidel, and Tilo Wiedera. “Inserting One Edge into a Simple Drawing Is
Hard.” Discrete and Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00394-9.
ieee: A. M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, and
T. Wiedera, “Inserting one edge into a simple drawing is hard,” Discrete and
Computational Geometry, vol. 69. Springer Nature, pp. 745–770, 2023.
ista: Arroyo Guevara AM, Klute F, Parada I, Vogtenhuber B, Seidel R, Wiedera T.
2023. Inserting one edge into a simple drawing is hard. Discrete and Computational
Geometry. 69, 745–770.
mla: Arroyo Guevara, Alan M., et al. “Inserting One Edge into a Simple Drawing Is
Hard.” Discrete and Computational Geometry, vol. 69, Springer Nature, 2023,
pp. 745–770, doi:10.1007/s00454-022-00394-9.
short: A.M. Arroyo Guevara, F. Klute, I. Parada, B. Vogtenhuber, R. Seidel, T. Wiedera,
Discrete and Computational Geometry 69 (2023) 745–770.
date_created: 2022-08-28T22:02:01Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2023-08-14T12:51:25Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1007/s00454-022-00394-9
ec_funded: 1
external_id:
arxiv:
- '1909.07347'
isi:
- '000840292800001'
file:
- access_level: open_access
checksum: def7ae3b28d9fd6aec16450e40090302
content_type: application/pdf
creator: alisjak
date_created: 2022-08-29T11:23:15Z
date_updated: 2022-08-29T11:23:15Z
file_id: '12006'
file_name: 2022_DiscreteandComputionalGeometry_Arroyo.pdf
file_size: 1002218
relation: main_file
success: 1
file_date_updated: 2022-08-29T11:23:15Z
has_accepted_license: '1'
intvolume: ' 69'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 745–770
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inserting one edge into a simple drawing is hard
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 69
year: '2023'
...
---
_id: '12563'
abstract:
- lang: eng
text: 'he approximate graph coloring problem, whose complexity is unresolved in
most cases, concerns finding a c-coloring of a graph that is promised to be k-colorable,
where c≥k. This problem naturally generalizes to promise graph homomorphism problems
and further to promise constraint satisfaction problems. The complexity of these
problems has recently been studied through an algebraic approach. In this paper,
we introduce two new techniques to analyze the complexity of promise CSPs: one
is based on topology and the other on adjunction. We apply these techniques, together
with the previously introduced algebraic approach, to obtain new unconditional
NP-hardness results for a significant class of approximate graph coloring and
promise graph homomorphism problems.'
acknowledgement: "Andrei Krokhin and Jakub Opršal were supported by the UK EPSRC grant
EP/R034516/1. Jakub Opršal has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No 101034413. Stanislav Živný was supported by a Royal Society University Research
Fellowship. This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 714532). The paper re\x1Eects only the authors’ views and not
the views of the ERC or the European Commission. "
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Andrei
full_name: Krokhin, Andrei
last_name: Krokhin
- first_name: Jakub
full_name: Opršal, Jakub
id: ec596741-c539-11ec-b829-c79322a91242
last_name: Opršal
orcid: 0000-0003-1245-3456
- first_name: Marcin
full_name: Wrochna, Marcin
last_name: Wrochna
- first_name: Stanislav
full_name: Živný, Stanislav
last_name: Živný
citation:
ama: Krokhin A, Opršal J, Wrochna M, Živný S. Topology and adjunction in promise
constraint satisfaction. SIAM Journal on Computing. 2023;52(1):38-79. doi:10.1137/20m1378223
apa: Krokhin, A., Opršal, J., Wrochna, M., & Živný, S. (2023). Topology and
adjunction in promise constraint satisfaction. SIAM Journal on Computing.
Society for Industrial & Applied Mathematics. https://doi.org/10.1137/20m1378223
chicago: Krokhin, Andrei, Jakub Opršal, Marcin Wrochna, and Stanislav Živný. “Topology
and Adjunction in Promise Constraint Satisfaction.” SIAM Journal on Computing.
Society for Industrial & Applied Mathematics, 2023. https://doi.org/10.1137/20m1378223.
ieee: A. Krokhin, J. Opršal, M. Wrochna, and S. Živný, “Topology and adjunction
in promise constraint satisfaction,” SIAM Journal on Computing, vol. 52,
no. 1. Society for Industrial & Applied Mathematics, pp. 38–79, 2023.
ista: Krokhin A, Opršal J, Wrochna M, Živný S. 2023. Topology and adjunction in
promise constraint satisfaction. SIAM Journal on Computing. 52(1), 38–79.
mla: Krokhin, Andrei, et al. “Topology and Adjunction in Promise Constraint Satisfaction.”
SIAM Journal on Computing, vol. 52, no. 1, Society for Industrial &
Applied Mathematics, 2023, pp. 38–79, doi:10.1137/20m1378223.
short: A. Krokhin, J. Opršal, M. Wrochna, S. Živný, SIAM Journal on Computing 52
(2023) 38–79.
date_created: 2023-02-16T07:03:52Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2023-08-01T13:11:30Z
day: '01'
department:
- _id: UlWa
doi: 10.1137/20m1378223
ec_funded: 1
external_id:
arxiv:
- '2003.11351'
isi:
- '000955000000001'
intvolume: ' 52'
isi: 1
issue: '1'
keyword:
- General Mathematics
- General Computer Science
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2003.11351
month: '01'
oa: 1
oa_version: Preprint
page: 38-79
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: SIAM Journal on Computing
publication_identifier:
eissn:
- 1095-7111
issn:
- 0097-5397
publication_status: published
publisher: Society for Industrial & Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topology and adjunction in promise constraint satisfaction
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 52
year: '2023'
...
---
_id: '12680'
abstract:
- lang: eng
text: The celebrated Erdős–Ko–Rado theorem about the maximal size of an intersecting
family of r-element subsets of was extended to the setting of exterior algebra
in [5, Theorem 2.3] and in [6, Theorem 1.4]. However, the equality case has not
been settled yet. In this short note, we show that the extension of the Erdős–Ko–Rado
theorem and the characterization of the equality case therein, as well as those
of the Hilton–Milner theorem to the setting of exterior algebra in the simplest
non-trivial case of two-forms follow from a folklore puzzle about possible arrangements
of an intersecting family of lines.
article_number: '113363'
article_processing_charge: No
article_type: letter_note
arxiv: 1
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
- first_name: Seyda
full_name: Köse, Seyda
id: 8ba3170d-dc85-11ea-9058-c4251c96a6eb
last_name: Köse
citation:
ama: Ivanov G, Köse S. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms. Discrete
Mathematics. 2023;346(6). doi:10.1016/j.disc.2023.113363
apa: Ivanov, G., & Köse, S. (2023). Erdős-Ko-Rado and Hilton-Milner theorems
for two-forms. Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.disc.2023.113363
chicago: Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems
for Two-Forms.” Discrete Mathematics. Elsevier, 2023. https://doi.org/10.1016/j.disc.2023.113363.
ieee: G. Ivanov and S. Köse, “Erdős-Ko-Rado and Hilton-Milner theorems for two-forms,”
Discrete Mathematics, vol. 346, no. 6. Elsevier, 2023.
ista: Ivanov G, Köse S. 2023. Erdős-Ko-Rado and Hilton-Milner theorems for two-forms.
Discrete Mathematics. 346(6), 113363.
mla: Ivanov, Grigory, and Seyda Köse. “Erdős-Ko-Rado and Hilton-Milner Theorems
for Two-Forms.” Discrete Mathematics, vol. 346, no. 6, 113363, Elsevier,
2023, doi:10.1016/j.disc.2023.113363.
short: G. Ivanov, S. Köse, Discrete Mathematics 346 (2023).
date_created: 2023-02-26T23:01:00Z
date_published: 2023-06-01T00:00:00Z
date_updated: 2023-10-04T11:54:57Z
day: '01'
department:
- _id: UlWa
- _id: GradSch
doi: 10.1016/j.disc.2023.113363
external_id:
arxiv:
- '2201.10892'
intvolume: ' 346'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2201.10892'
month: '06'
oa: 1
oa_version: Preprint
publication: Discrete Mathematics
publication_identifier:
issn:
- 0012-365X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '13331'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Erdős-Ko-Rado and Hilton-Milner theorems for two-forms
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 346
year: '2023'
...
---
_id: '12833'
abstract:
- lang: eng
text: 'The input to the token swapping problem is a graph with vertices v1, v2,
. . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal
is to get token i to vertex vi for all i= 1, . . . , n using a minimum number
of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token
swapping on a tree, also known as “sorting with a transposition tree,” is not
known to be in P nor NP-complete. We present some partial results: 1. An optimum
swap sequence may need to perform a swap on a leaf vertex that has the correct
token (a “happy leaf”), disproving a conjecture of Vaughan. 2. Any algorithm that
fixes happy leaves—as all known approximation algorithms for the problem do—has
approximation factor at least 4/3. Furthermore, the two best-known 2-approximation
algorithms have approximation factor exactly 2. 3. A generalized problem—weighted
coloured token swapping—is NP-complete on trees, but solvable in polynomial time
on paths and stars. In this version, tokens and vertices have colours, and colours
have weights. The goal is to get every token to a vertex of the same colour, and
the cost of a swap is the sum of the weights of the two tokens involved.'
acknowledgement: "This work was begun at the University of Waterloo and was partially
supported by the Natural Sciences and Engineering Council of Canada (NSERC).\r\n"
article_number: '9'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ahmad
full_name: Biniaz, Ahmad
last_name: Biniaz
- first_name: Kshitij
full_name: Jain, Kshitij
last_name: Jain
- first_name: Anna
full_name: Lubiw, Anna
last_name: Lubiw
- first_name: Zuzana
full_name: Masárová, Zuzana
id: 45CFE238-F248-11E8-B48F-1D18A9856A87
last_name: Masárová
orcid: 0000-0002-6660-1322
- first_name: Tillmann
full_name: Miltzow, Tillmann
last_name: Miltzow
- first_name: Debajyoti
full_name: Mondal, Debajyoti
last_name: Mondal
- first_name: Anurag Murty
full_name: Naredla, Anurag Murty
last_name: Naredla
- first_name: Josef
full_name: Tkadlec, Josef
id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87
last_name: Tkadlec
orcid: 0000-0002-1097-9684
- first_name: Alexi
full_name: Turcotte, Alexi
last_name: Turcotte
citation:
ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. Discrete Mathematics
and Theoretical Computer Science. 2023;24(2). doi:10.46298/DMTCS.8383
apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte,
A. (2023). Token swapping on trees. Discrete Mathematics and Theoretical Computer
Science. EPI Sciences. https://doi.org/10.46298/DMTCS.8383
chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow,
Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token
Swapping on Trees.” Discrete Mathematics and Theoretical Computer Science.
EPI Sciences, 2023. https://doi.org/10.46298/DMTCS.8383.
ieee: A. Biniaz et al., “Token swapping on trees,” Discrete Mathematics
and Theoretical Computer Science, vol. 24, no. 2. EPI Sciences, 2023.
ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec
J, Turcotte A. 2023. Token swapping on trees. Discrete Mathematics and Theoretical
Computer Science. 24(2), 9.
mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” Discrete Mathematics and
Theoretical Computer Science, vol. 24, no. 2, 9, EPI Sciences, 2023, doi:10.46298/DMTCS.8383.
short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla,
J. Tkadlec, A. Turcotte, Discrete Mathematics and Theoretical Computer Science
24 (2023).
date_created: 2023-04-16T22:01:08Z
date_published: 2023-01-18T00:00:00Z
date_updated: 2024-01-04T12:42:09Z
day: '18'
ddc:
- '000'
department:
- _id: KrCh
- _id: HeEd
- _id: UlWa
doi: 10.46298/DMTCS.8383
external_id:
arxiv:
- '1903.06981'
file:
- access_level: open_access
checksum: 439102ea4f6e2aeefd7107dfb9ccf532
content_type: application/pdf
creator: dernst
date_created: 2023-04-17T08:10:28Z
date_updated: 2023-04-17T08:10:28Z
file_id: '12844'
file_name: 2022_DMTCS_Biniaz.pdf
file_size: 2072197
relation: main_file
success: 1
file_date_updated: 2023-04-17T08:10:28Z
has_accepted_license: '1'
intvolume: ' 24'
issue: '2'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
publication: Discrete Mathematics and Theoretical Computer Science
publication_identifier:
eissn:
- 1365-8050
issn:
- 1462-7264
publication_status: published
publisher: EPI Sciences
quality_controlled: '1'
related_material:
record:
- id: '7950'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Token swapping on trees
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '10776'
abstract:
- lang: eng
text: 'Let K be a convex body in Rn (i.e., a compact convex set with nonempty interior).
Given a point p in the interior of K, a hyperplane h passing through p is called
barycentric if p is the barycenter of K∩h. In 1961, Grünbaum raised the question
whether, for every K, there exists an interior point p through which there are
at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly
resolved affirmatively by showing that this is the case if p=p0 is the point of
maximal depth in K. However, while working on a related question, we noticed that
one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample;
this re-opens Grünbaum’s question. It follows from known results that for n≥2,
there are always at least three distinct barycentric cuts through the point p0∈K
of maximal depth. Using tools related to Morse theory we are able to improve this
bound: four distinct barycentric cuts through p0 are guaranteed if n≥3.'
acknowledgement: The work by Zuzana Patáková has been partially supported by Charles
University Research Center Program No. UNCE/SCI/022, and part of it was done during
her research stay at IST Austria. The work by Martin Tancer is supported by the
GAČR Grant 19-04113Y and by the Charles University Projects PRIMUS/17/SCI/3 and
UNCE/SCI/004.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zuzana
full_name: Patakova, Zuzana
id: 48B57058-F248-11E8-B48F-1D18A9856A87
last_name: Patakova
orcid: 0000-0002-3975-1683
- first_name: Martin
full_name: Tancer, Martin
last_name: Tancer
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Patakova Z, Tancer M, Wagner U. Barycentric cuts through a convex body. Discrete
and Computational Geometry. 2022;68:1133-1154. doi:10.1007/s00454-021-00364-7
apa: Patakova, Z., Tancer, M., & Wagner, U. (2022). Barycentric cuts through
a convex body. Discrete and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-021-00364-7
chicago: Patakova, Zuzana, Martin Tancer, and Uli Wagner. “Barycentric Cuts through
a Convex Body.” Discrete and Computational Geometry. Springer Nature, 2022.
https://doi.org/10.1007/s00454-021-00364-7.
ieee: Z. Patakova, M. Tancer, and U. Wagner, “Barycentric cuts through a convex
body,” Discrete and Computational Geometry, vol. 68. Springer Nature, pp.
1133–1154, 2022.
ista: Patakova Z, Tancer M, Wagner U. 2022. Barycentric cuts through a convex body.
Discrete and Computational Geometry. 68, 1133–1154.
mla: Patakova, Zuzana, et al. “Barycentric Cuts through a Convex Body.” Discrete
and Computational Geometry, vol. 68, Springer Nature, 2022, pp. 1133–54, doi:10.1007/s00454-021-00364-7.
short: Z. Patakova, M. Tancer, U. Wagner, Discrete and Computational Geometry 68
(2022) 1133–1154.
date_created: 2022-02-20T23:01:35Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-02T14:38:58Z
day: '01'
department:
- _id: UlWa
doi: 10.1007/s00454-021-00364-7
external_id:
arxiv:
- '2003.13536'
isi:
- '000750681500001'
intvolume: ' 68'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2003.13536
month: '12'
oa: 1
oa_version: Preprint
page: 1133-1154
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Barycentric cuts through a convex body
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 68
year: '2022'
...
---
_id: '10887'
abstract:
- lang: eng
text: "We introduce a new way of representing logarithmically concave functions
on Rd. It allows us to extend the notion of the largest volume ellipsoid contained
in a convex body to the setting of logarithmically concave functions as follows.
For every s>0, we define a class of non-negative functions on Rd derived from
ellipsoids in Rd+1. For any log-concave function f on Rd , and any fixed s>0,
we consider functions belonging to this class, and find the one with the largest
integral under the condition that it is pointwise less than or equal to f, and
we call it the John s-function of f. After establishing existence and uniqueness,
we give a characterization of this function similar to the one given by John in
his fundamental theorem. We find that John s-functions converge to characteristic
functions of ellipsoids as s tends to zero and to Gaussian densities as s tends
to infinity.\r\nAs an application, we prove a quantitative Helly type result:
the integral of the pointwise minimum of any family of log-concave functions is
at least a constant cd multiple of the integral of the pointwise minimum of a
properly chosen subfamily of size 3d+2, where cd depends only on d."
acknowledgement: 'G.I. was supported by the Ministry of Education and Science of the
Russian Federation in the framework of MegaGrant no 075-15-2019-1926. M.N. was supported
by the National Research, Development and Innovation Fund (NRDI) grants K119670
and KKP-133864 as well as the Bolyai Scholarship of the Hungarian Academy of Sciences
and the New National Excellence Programme and the TKP2020-NKA-06 program provided
by the NRDI. '
article_number: '109441'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
- first_name: Márton
full_name: Naszódi, Márton
last_name: Naszódi
citation:
ama: Ivanov G, Naszódi M. Functional John ellipsoids. Journal of Functional Analysis.
2022;282(11). doi:10.1016/j.jfa.2022.109441
apa: Ivanov, G., & Naszódi, M. (2022). Functional John ellipsoids. Journal
of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109441
chicago: Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” Journal
of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109441.
ieee: G. Ivanov and M. Naszódi, “Functional John ellipsoids,” Journal of Functional
Analysis, vol. 282, no. 11. Elsevier, 2022.
ista: Ivanov G, Naszódi M. 2022. Functional John ellipsoids. Journal of Functional
Analysis. 282(11), 109441.
mla: Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” Journal
of Functional Analysis, vol. 282, no. 11, 109441, Elsevier, 2022, doi:10.1016/j.jfa.2022.109441.
short: G. Ivanov, M. Naszódi, Journal of Functional Analysis 282 (2022).
date_created: 2022-03-20T23:01:38Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-08-02T14:51:11Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1016/j.jfa.2022.109441
external_id:
arxiv:
- '2006.09934'
isi:
- '000781371300008'
file:
- access_level: open_access
checksum: 1cf185e264e04c87cb1ce67a00db88ab
content_type: application/pdf
creator: dernst
date_created: 2022-08-02T10:40:48Z
date_updated: 2022-08-02T10:40:48Z
file_id: '11721'
file_name: 2022_JourFunctionalAnalysis_Ivanov.pdf
file_size: 734482
relation: main_file
success: 1
file_date_updated: 2022-08-02T10:40:48Z
has_accepted_license: '1'
intvolume: ' 282'
isi: 1
issue: '11'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functional John ellipsoids
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 282
year: '2022'
...
---
_id: '11185'
abstract:
- lang: eng
text: Bundling crossings is a strategy which can enhance the readability of graph
drawings. In this paper we consider bundlings for families of pseudosegments,
i.e., simple curves such that any two have share at most one point at which they
cross. Our main result is that there is a polynomial-time algorithm to compute
an 8-approximation of the bundled crossing number of such instances (up to adding
a term depending on the facial structure). This 8-approximation also holds for
bundlings of good drawings of graphs. In the special case of circular drawings
the approximation factor is 8 (no extra term), this improves upon the 10-approximation
of Fink et al. [6]. We also show how to compute a 92-approximation when the intersection
graph of the pseudosegments is bipartite.
acknowledgement: This work was initiated during the Workshop on Geometric Graphs in
November 2019 in Strobl, Austria. We would like to thank Oswin Aichholzer, Fabian
Klute, Man-Kwun Chiu, Martin Balko, Pavel Valtr for their avid discussions during
the workshop. The first author has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Sklodowska Curie grant agreement
No 754411. The second author has been supported by the German Research Foundation
DFG Project FE 340/12-1.
article_processing_charge: No
arxiv: 1
author:
- first_name: Alan M
full_name: Arroyo Guevara, Alan M
id: 3207FDC6-F248-11E8-B48F-1D18A9856A87
last_name: Arroyo Guevara
orcid: 0000-0003-2401-8670
- first_name: Stefan
full_name: Felsner, Stefan
last_name: Felsner
citation:
ama: 'Arroyo Guevara AM, Felsner S. Approximating the bundled crossing number. In:
WALCOM 2022: Algorithms and Computation. Vol 13174. LNCS. Springer Nature;
2022:383-395. doi:10.1007/978-3-030-96731-4_31'
apa: 'Arroyo Guevara, A. M., & Felsner, S. (2022). Approximating the bundled
crossing number. In WALCOM 2022: Algorithms and Computation (Vol. 13174,
pp. 383–395). Jember, Indonesia: Springer Nature. https://doi.org/10.1007/978-3-030-96731-4_31'
chicago: 'Arroyo Guevara, Alan M, and Stefan Felsner. “Approximating the Bundled
Crossing Number.” In WALCOM 2022: Algorithms and Computation, 13174:383–95.
LNCS. Springer Nature, 2022. https://doi.org/10.1007/978-3-030-96731-4_31.'
ieee: 'A. M. Arroyo Guevara and S. Felsner, “Approximating the bundled crossing
number,” in WALCOM 2022: Algorithms and Computation, Jember, Indonesia,
2022, vol. 13174, pp. 383–395.'
ista: 'Arroyo Guevara AM, Felsner S. 2022. Approximating the bundled crossing number.
WALCOM 2022: Algorithms and Computation. WALCOM: Algorithms and ComputationLNCS
vol. 13174, 383–395.'
mla: 'Arroyo Guevara, Alan M., and Stefan Felsner. “Approximating the Bundled Crossing
Number.” WALCOM 2022: Algorithms and Computation, vol. 13174, Springer
Nature, 2022, pp. 383–95, doi:10.1007/978-3-030-96731-4_31.'
short: 'A.M. Arroyo Guevara, S. Felsner, in:, WALCOM 2022: Algorithms and Computation,
Springer Nature, 2022, pp. 383–395.'
conference:
end_date: 2022-03-26
location: Jember, Indonesia
name: 'WALCOM: Algorithms and Computation'
start_date: 2022-03-24
date_created: 2022-04-17T22:01:47Z
date_published: 2022-03-16T00:00:00Z
date_updated: 2023-09-25T10:56:10Z
day: '16'
department:
- _id: UlWa
doi: 10.1007/978-3-030-96731-4_31
ec_funded: 1
external_id:
arxiv:
- '2109.14892'
intvolume: ' 13174'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2109.14892'
month: '03'
oa: 1
oa_version: Preprint
page: 383-395
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 'WALCOM 2022: Algorithms and Computation'
publication_identifier:
eissn:
- 1611-3349
isbn:
- '9783030967307'
issn:
- 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '13969'
relation: later_version
status: public
scopus_import: '1'
series_title: LNCS
status: public
title: Approximating the bundled crossing number
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 13174
year: '2022'
...
---
_id: '11435'
abstract:
- lang: eng
text: 'We introduce a new variant of quantitative Helly-type theorems: the minimal
homothetic distance of the intersection of a family of convex sets to the intersection
of a subfamily of a fixed size. As an application, we establish the following
quantitative Helly-type result for the diameter. If $K$ is the intersection of
finitely many convex bodies in $\mathbb{R}^d$, then one can select $2d$ of these
bodies whose intersection is of diameter at most $(2d)^3{diam}(K)$. The best previously
known estimate, due to Brazitikos [Bull. Hellenic Math. Soc., 62 (2018), pp. 19--25],
is $c d^{11/2}$. Moreover, we confirm that the multiplicative factor $c d^{1/2}$
conjectured by Bárány, Katchalski, and Pach [Proc. Amer. Math. Soc., 86 (1982),
pp. 109--114] cannot be improved. The bounds above follow from our key result
that concerns sparse approximation of a convex polytope by the convex hull of
a well-chosen subset of its vertices: Assume that $Q \subset {\mathbb R}^d$ is
a polytope whose centroid is the origin. Then there exist at most 2d vertices
of $Q$ whose convex hull $Q^{\prime \prime}$ satisfies $Q \subset - 8d^3 Q^{\prime
\prime}.$'
acknowledgement: "G.I. acknowledges the financial support from the Ministry of Educational
and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926.
M.N. was supported by the National Research, Development and Innovation Fund (NRDI)
grants K119670 and\r\nKKP-133864 as well as the Bolyai Scholarship of the Hungarian
Academy of Sciences and the New National Excellence Programme and the TKP2020-NKA-06
program provided by the NRDI."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
- first_name: Marton
full_name: Naszodi, Marton
last_name: Naszodi
citation:
ama: 'Ivanov G, Naszodi M. A quantitative Helly-type theorem: Containment in a homothet.
SIAM Journal on Discrete Mathematics. 2022;36(2):951-957. doi:10.1137/21M1403308'
apa: 'Ivanov, G., & Naszodi, M. (2022). A quantitative Helly-type theorem: Containment
in a homothet. SIAM Journal on Discrete Mathematics. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/21M1403308'
chicago: 'Ivanov, Grigory, and Marton Naszodi. “A Quantitative Helly-Type Theorem:
Containment in a Homothet.” SIAM Journal on Discrete Mathematics. Society
for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21M1403308.'
ieee: 'G. Ivanov and M. Naszodi, “A quantitative Helly-type theorem: Containment
in a homothet,” SIAM Journal on Discrete Mathematics, vol. 36, no. 2. Society
for Industrial and Applied Mathematics, pp. 951–957, 2022.'
ista: 'Ivanov G, Naszodi M. 2022. A quantitative Helly-type theorem: Containment
in a homothet. SIAM Journal on Discrete Mathematics. 36(2), 951–957.'
mla: 'Ivanov, Grigory, and Marton Naszodi. “A Quantitative Helly-Type Theorem: Containment
in a Homothet.” SIAM Journal on Discrete Mathematics, vol. 36, no. 2, Society
for Industrial and Applied Mathematics, 2022, pp. 951–57, doi:10.1137/21M1403308.'
short: G. Ivanov, M. Naszodi, SIAM Journal on Discrete Mathematics 36 (2022) 951–957.
date_created: 2022-06-05T22:01:50Z
date_published: 2022-04-11T00:00:00Z
date_updated: 2023-10-18T06:58:03Z
day: '11'
department:
- _id: UlWa
doi: 10.1137/21M1403308
external_id:
arxiv:
- '2103.04122'
isi:
- '000793158200002'
intvolume: ' 36'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2103.04122'
month: '04'
oa: 1
oa_version: Preprint
page: 951-957
publication: SIAM Journal on Discrete Mathematics
publication_identifier:
issn:
- 0895-4801
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'A quantitative Helly-type theorem: Containment in a homothet'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 36
year: '2022'
...
---
_id: '11593'
abstract:
- lang: eng
text: 'A drawing of a graph on a surface is independently even if every pair of
nonadjacent edges in the drawing crosses an even number of times. The Z2 -genus
of a graph G is the minimum g such that G has an independently even drawing on
the orientable surface of genus g. An unpublished result by Robertson and Seymour
implies that for every t, every graph of sufficiently large genus contains as
a minor a projective t×t grid or one of the following so-called t -Kuratowski
graphs: K3,t, or t copies of K5 or K3,3 sharing at most two common vertices. We
show that the Z2-genus of graphs in these families is unbounded in t; in fact,
equal to their genus. Together, this implies that the genus of a graph is bounded
from above by a function of its Z2-genus, solving a problem posed by Schaefer
and Štefankovič, and giving an approximate version of the Hanani–Tutte theorem
on orientable surfaces. We also obtain an analogous result for Euler genus and
Euler Z2-genus of graphs.'
acknowledgement: "We thank Zdeněk Dvořák, Xavier Goaoc, and Pavel Paták for helpful
discussions. We also thank Bojan Mohar, Paul Seymour, Gelasio Salazar, Jim Geelen,
and John Maharry for information about their unpublished results related to Conjecture
3.1. Finally we thank the reviewers for corrections and suggestions for improving
the presentation.\r\nSupported by Austrian Science Fund (FWF): M2281-N35. Supported
by project 19-04113Y of the Czech Science Foundation (GAČR), by the Czech-French
collaboration project EMBEDS II (CZ: 7AMB17FR029, FR: 38087RM), and by Charles University
project UNCE/SCI/004."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Radoslav
full_name: Fulek, Radoslav
id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87
last_name: Fulek
orcid: 0000-0001-8485-1774
- first_name: Jan
full_name: Kynčl, Jan
last_name: Kynčl
citation:
ama: Fulek R, Kynčl J. The Z2-Genus of Kuratowski minors. Discrete and Computational
Geometry. 2022;68:425-447. doi:10.1007/s00454-022-00412-w
apa: Fulek, R., & Kynčl, J. (2022). The Z2-Genus of Kuratowski minors. Discrete
and Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00412-w
chicago: Fulek, Radoslav, and Jan Kynčl. “The Z2-Genus of Kuratowski Minors.” Discrete
and Computational Geometry. Springer Nature, 2022. https://doi.org/10.1007/s00454-022-00412-w.
ieee: R. Fulek and J. Kynčl, “The Z2-Genus of Kuratowski minors,” Discrete and
Computational Geometry, vol. 68. Springer Nature, pp. 425–447, 2022.
ista: Fulek R, Kynčl J. 2022. The Z2-Genus of Kuratowski minors. Discrete and Computational
Geometry. 68, 425–447.
mla: Fulek, Radoslav, and Jan Kynčl. “The Z2-Genus of Kuratowski Minors.” Discrete
and Computational Geometry, vol. 68, Springer Nature, 2022, pp. 425–47, doi:10.1007/s00454-022-00412-w.
short: R. Fulek, J. Kynčl, Discrete and Computational Geometry 68 (2022) 425–447.
date_created: 2022-07-17T22:01:56Z
date_published: 2022-09-01T00:00:00Z
date_updated: 2023-08-14T12:43:52Z
day: '01'
department:
- _id: UlWa
doi: 10.1007/s00454-022-00412-w
external_id:
arxiv:
- '1803.05085'
isi:
- '000825014500001'
intvolume: ' 68'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1803.05085
month: '09'
oa: 1
oa_version: Preprint
page: 425-447
project:
- _id: 261FA626-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02281
name: Eliminating intersections in drawings of graphs
publication: Discrete and Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '186'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: The Z2-Genus of Kuratowski minors
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2022'
...
---
_id: '11777'
abstract:
- lang: eng
text: "In this dissertation we study coboundary expansion of simplicial complex
with a view of giving geometric applications.\r\nOur main novel tool is an equivariant
version of Gromov's celebrated Topological Overlap Theorem. The equivariant topological
overlap theorem leads to various geometric applications including a quantitative
non-embeddability result for sufficiently thick buildings (which partially resolves
a conjecture of Tancer and Vorwerk) and an improved lower bound on the pair-crossing
number of (bounded degree) expander graphs. Additionally, we will give new proofs
for several known lower bounds for geometric problems such as the number of Tverberg
partitions or the crossing number of complete bipartite graphs.\r\nFor the aforementioned
applications one is naturally lead to study expansion properties of joins of simplicial
complexes. In the presence of a special certificate for expansion (as it is the
case, e.g., for spherical buildings), the join of two expanders is an expander.
On the flip-side, we report quite some evidence that coboundary expansion exhibits
very non-product-like behaviour under taking joins. For instance, we exhibit infinite
families of graphs $(G_n)_{n\\in \\mathbb{N}}$ and $(H_n)_{n\\in\\mathbb{N}}$
whose join $G_n*H_n$ has expansion of lower order than the product of the expansion
constant of the graphs. Moreover, we show an upper bound of $(d+1)/2^d$ on the
normalized coboundary expansion constants for the complete multipartite complex
$[n]^{*(d+1)}$ (under a mild divisibility condition on $n$).\r\nVia the probabilistic
method the latter result extends to an upper bound of $(d+1)/2^d+\\varepsilon$
on the coboundary expansion constant of the spherical building associated with
$\\mathrm{PGL}_{d+2}(\\mathbb{F}_q)$ for any $\\varepsilon>0$ and sufficiently
large $q=q(\\varepsilon)$. This disproves a conjecture of Lubotzky, Meshulam and
Mozes -- in a rather strong sense.\r\nBy improving on existing lower bounds we
make further progress towards closing the gap between the known lower and upper
bounds on the coboundary expansion constants of $[n]^{*(d+1)}$. The best improvements
we achieve using computer-aided proofs and flag algebras. The exact value even
for the complete $3$-partite $2$-dimensional complex $[n]^{*3}$ remains unknown
but we are happy to conjecture a precise value for every $n$. %Moreover, we show
that a previously shown lower bound on the expansion constant of the spherical
building associated with $\\mathrm{PGL}_{2}(\\mathbb{F}_q)$ is not tight.\r\nIn
a loosely structured, last chapter of this thesis we collect further smaller observations
related to expansion. We point out a link between discrete Morse theory and a
technique for showing coboundary expansion, elaborate a bit on the hardness of
computing coboundary expansion constants, propose a new criterion for coboundary
expansion (in a very dense setting) and give one way of making the folklore result
that expansion of links is a necessary condition for a simplicial complex to be
an expander precise."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Pascal
full_name: Wild, Pascal
id: 4C20D868-F248-11E8-B48F-1D18A9856A87
last_name: Wild
citation:
ama: Wild P. High-dimensional expansion and crossing numbers of simplicial complexes.
2022. doi:10.15479/at:ista:11777
apa: Wild, P. (2022). High-dimensional expansion and crossing numbers of simplicial
complexes. Institute of Science and Technology. https://doi.org/10.15479/at:ista:11777
chicago: Wild, Pascal. “High-Dimensional Expansion and Crossing Numbers of Simplicial
Complexes.” Institute of Science and Technology, 2022. https://doi.org/10.15479/at:ista:11777.
ieee: P. Wild, “High-dimensional expansion and crossing numbers of simplicial complexes,”
Institute of Science and Technology, 2022.
ista: Wild P. 2022. High-dimensional expansion and crossing numbers of simplicial
complexes. Institute of Science and Technology.
mla: Wild, Pascal. High-Dimensional Expansion and Crossing Numbers of Simplicial
Complexes. Institute of Science and Technology, 2022, doi:10.15479/at:ista:11777.
short: P. Wild, High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes,
Institute of Science and Technology, 2022.
date_created: 2022-08-10T15:51:19Z
date_published: 2022-08-11T00:00:00Z
date_updated: 2023-06-22T09:56:36Z
day: '11'
ddc:
- '500'
- '516'
- '514'
degree_awarded: PhD
department:
- _id: GradSch
- _id: UlWa
doi: 10.15479/at:ista:11777
ec_funded: 1
file:
- access_level: open_access
checksum: f5f3af1fb7c8a24b71ddc88ad7f7c5b4
content_type: text/x-python
creator: pwild
date_created: 2022-08-10T15:34:04Z
date_updated: 2022-08-10T15:34:04Z
description: Code for computer-assisted proofs in Section 8.4.7 in Thesis
file_id: '11780'
file_name: flags.py
file_size: 16828
relation: supplementary_material
- access_level: open_access
checksum: 1f7c12dfe3bdaa9b147e4fbc3d34e3d5
content_type: text/x-c++src
creator: pwild
date_created: 2022-08-10T15:34:10Z
date_updated: 2022-08-10T15:34:10Z
description: Code for proof of Lemma 8.20 in Thesis
file_id: '11781'
file_name: lowerbound.cpp
file_size: 12226
relation: supplementary_material
- access_level: open_access
checksum: 4cf81455c49e5dec3b9b2e3980137eeb
content_type: text/x-python
creator: pwild
date_created: 2022-08-10T15:34:17Z
date_updated: 2022-08-10T15:34:17Z
description: Code for proof of Proposition 7.9 in Thesis
file_id: '11782'
file_name: upperbound.py
file_size: 3240
relation: supplementary_material
- access_level: open_access
checksum: 4e96575b10cbe4e0d0db2045b2847774
content_type: application/pdf
creator: pwild
date_created: 2022-08-11T16:08:33Z
date_updated: 2022-08-11T16:08:33Z
file_id: '11809'
file_name: finalthesisPascalWildPDFA.pdf
file_size: 5086282
relation: main_file
title: High-Dimensional Expansion and Crossing Numbers of Simplicial Complexes
- access_level: closed
checksum: 92d94842a1fb6dca5808448137573b2e
content_type: application/zip
creator: pwild
date_created: 2022-08-11T16:09:19Z
date_updated: 2022-08-11T16:09:19Z
file_id: '11810'
file_name: ThesisSubmission.zip
file_size: 18150068
relation: source_file
file_date_updated: 2022-08-11T16:09:19Z
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: '170'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication_identifier:
isbn:
- 978-3-99078-021-3
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology
status: public
supervisor:
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
title: High-dimensional expansion and crossing numbers of simplicial complexes
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2022'
...