---
_id: '742'
abstract:
- lang: eng
text: 'We give a detailed and easily accessible proof of Gromov’s Topological Overlap
Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral
cell complex of dimension d. Informally, the theorem states that if X has sufficiently
strong higher-dimensional expansion properties (which generalize edge expansion
of graphs and are defined in terms of cellular cochains of X) then X has the following
topological overlap property: for every continuous map (Formula presented.) there
exists a point (Formula presented.) that is contained in the images of a positive
fraction (Formula presented.) of the d-cells of X. More generally, the conclusion
holds if (Formula presented.) is replaced by any d-dimensional piecewise-linear
manifold M, with a constant (Formula presented.) that depends only on d and on
the expansion properties of X, but not on M.'
article_processing_charge: Yes (via OA deal)
author:
- first_name: Dominic
full_name: Dotterrer, Dominic
last_name: Dotterrer
- first_name: Tali
full_name: Kaufman, Tali
last_name: Kaufman
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Dotterrer D, Kaufman T, Wagner U. On expansion and topological overlap. Geometriae
Dedicata. 2018;195(1):307–317. doi:10.1007/s10711-017-0291-4
apa: Dotterrer, D., Kaufman, T., & Wagner, U. (2018). On expansion and topological
overlap. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0291-4
chicago: Dotterrer, Dominic, Tali Kaufman, and Uli Wagner. “On Expansion and Topological
Overlap.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0291-4.
ieee: D. Dotterrer, T. Kaufman, and U. Wagner, “On expansion and topological overlap,”
Geometriae Dedicata, vol. 195, no. 1. Springer, pp. 307–317, 2018.
ista: Dotterrer D, Kaufman T, Wagner U. 2018. On expansion and topological overlap.
Geometriae Dedicata. 195(1), 307–317.
mla: Dotterrer, Dominic, et al. “On Expansion and Topological Overlap.” Geometriae
Dedicata, vol. 195, no. 1, Springer, 2018, pp. 307–317, doi:10.1007/s10711-017-0291-4.
short: D. Dotterrer, T. Kaufman, U. Wagner, Geometriae Dedicata 195 (2018) 307–317.
date_created: 2018-12-11T11:48:16Z
date_published: 2018-08-01T00:00:00Z
date_updated: 2023-09-27T12:29:57Z
day: '01'
ddc:
- '514'
- '516'
department:
- _id: UlWa
doi: 10.1007/s10711-017-0291-4
external_id:
isi:
- '000437122700017'
file:
- access_level: open_access
checksum: d2f70fc132156504aa4c626aa378a7ab
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creator: kschuh
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file_name: s10711-017-0291-4.pdf
file_size: 412486
relation: main_file
file_date_updated: 2020-07-14T12:47:58Z
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intvolume: ' 195'
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month: '08'
oa: 1
oa_version: Published Version
page: 307–317
project:
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grant_number: PP00P2_138948
name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics'
publication: Geometriae Dedicata
publication_status: published
publisher: Springer
publist_id: '6925'
pubrep_id: '912'
quality_controlled: '1'
related_material:
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relation: earlier_version
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scopus_import: '1'
status: public
title: On expansion and topological overlap
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 195
year: '2018'
...
---
_id: '1378'
abstract:
- lang: eng
text: 'We give a detailed and easily accessible proof of Gromov''s Topological Overlap
Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral
cell complex of dimension d. Informally, the theorem states that if X has sufficiently
strong higher-dimensional expansion properties (which generalize edge expansion
of graphs and are defined in terms of cellular cochains of X) then X has the following
topological overlap property: for every continuous map X → ℝd there exists a point
p ∈ ℝd whose preimage intersects a positive fraction μ > 0 of the d-cells of
X. More generally, the conclusion holds if ℝd is replaced by any d-dimensional
piecewise-linear (PL) manifold M, with a constant μ that depends only on d and
on the expansion properties of X, but not on M.'
alternative_title:
- LIPIcs
author:
- first_name: Dominic
full_name: Dotterrer, Dominic
last_name: Dotterrer
- first_name: Tali
full_name: Kaufman, Tali
last_name: Kaufman
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Dotterrer D, Kaufman T, Wagner U. On expansion and topological overlap. In:
Vol 51. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing;
2016:35.1-35.10. doi:10.4230/LIPIcs.SoCG.2016.35'
apa: 'Dotterrer, D., Kaufman, T., & Wagner, U. (2016). On expansion and topological
overlap (Vol. 51, p. 35.1-35.10). Presented at the SoCG: Symposium on Computational
Geometry, Medford, MA, USA: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH,
Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SoCG.2016.35'
chicago: Dotterrer, Dominic, Tali Kaufman, and Uli Wagner. “On Expansion and Topological
Overlap,” 51:35.1-35.10. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH,
Dagstuhl Publishing, 2016. https://doi.org/10.4230/LIPIcs.SoCG.2016.35.
ieee: 'D. Dotterrer, T. Kaufman, and U. Wagner, “On expansion and topological overlap,”
presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA,
2016, vol. 51, p. 35.1-35.10.'
ista: 'Dotterrer D, Kaufman T, Wagner U. 2016. On expansion and topological overlap.
SoCG: Symposium on Computational Geometry, LIPIcs, vol. 51, 35.1-35.10.'
mla: Dotterrer, Dominic, et al. On Expansion and Topological Overlap. Vol.
51, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing,
2016, p. 35.1-35.10, doi:10.4230/LIPIcs.SoCG.2016.35.
short: D. Dotterrer, T. Kaufman, U. Wagner, in:, Schloss Dagstuhl- Leibniz-Zentrum
fur Informatik GmbH, Dagstuhl Publishing, 2016, p. 35.1-35.10.
conference:
end_date: 2016-06-17
location: Medford, MA, USA
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2016-06-14
date_created: 2018-12-11T11:51:41Z
date_published: 2016-06-01T00:00:00Z
date_updated: 2023-09-27T12:29:56Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2016.35
file:
- access_level: open_access
checksum: cee65b0e722d50f9d1cc70c90ec1d59b
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:38Z
date_updated: 2020-07-14T12:44:47Z
file_id: '4699'
file_name: IST-2016-623-v1+1_LIPIcs-SoCG-2016-35.pdf
file_size: 536923
relation: main_file
file_date_updated: 2020-07-14T12:44:47Z
has_accepted_license: '1'
intvolume: ' 51'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 35.1 - 35.10
project:
- _id: 25FA3206-B435-11E9-9278-68D0E5697425
grant_number: PP00P2_138948
name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics'
publication_status: published
publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
publist_id: '5833'
pubrep_id: '623'
quality_controlled: '1'
related_material:
record:
- id: '742'
relation: later_version
status: public
scopus_import: 1
status: public
title: On expansion and topological overlap
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: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2016'
...
---
_id: '1381'
abstract:
- lang: eng
text: 'Motivated by Tverberg-type problems in topological combinatorics and by classical
results about embeddings (maps without double points), we study the question whether
a finite simplicial complex K can be mapped into double-struck Rd without higher-multiplicity
intersections. We focus on conditions for the existence of almost r-embeddings,
i.e., maps f : K → double-struck Rd such that f(σ1) ∩ ⋯ ∩ f(σr) = ∅ whenever σ1,
..., σr are pairwise disjoint simplices of K. Generalizing the classical Haefliger-Weber
embeddability criterion, we show that a well-known necessary deleted product condition
for the existence of almost r-embeddings is sufficient in a suitable r-metastable
range of dimensions: If rd ≥ (r + 1) dim K + 3, then there exists an almost r-embedding
K → double-struck Rd if and only if there exists an equivariant map (K)Δ r → Sr
Sd(r-1)-1, where (K)Δ r is the deleted r-fold product of K, the target Sd(r-1)-1
is the sphere of dimension d(r - 1) - 1, and Sr is the symmetric group. This significantly
extends one of the main results of our previous paper (which treated the special
case where d = rk and dim K = (r - 1)k for some k ≥ 3), and settles an open question
raised there.'
alternative_title:
- LIPIcs
author:
- first_name: Isaac
full_name: Mabillard, Isaac
id: 32BF9DAA-F248-11E8-B48F-1D18A9856A87
last_name: Mabillard
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Mabillard I, Wagner U. Eliminating higher-multiplicity intersections, II.
The deleted product criterion in the r-metastable range. In: Vol 51. Schloss Dagstuhl-
Leibniz-Zentrum fur Informatik GmbH; 2016:51.1-51.12. doi:10.4230/LIPIcs.SoCG.2016.51'
apa: 'Mabillard, I., & Wagner, U. (2016). Eliminating higher-multiplicity intersections,
II. The deleted product criterion in the r-metastable range (Vol. 51, p. 51.1-51.12).
Presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA:
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH. https://doi.org/10.4230/LIPIcs.SoCG.2016.51'
chicago: Mabillard, Isaac, and Uli Wagner. “Eliminating Higher-Multiplicity Intersections,
II. The Deleted Product Criterion in the r-Metastable Range,” 51:51.1-51.12. Schloss
Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016. https://doi.org/10.4230/LIPIcs.SoCG.2016.51.
ieee: 'I. Mabillard and U. Wagner, “Eliminating higher-multiplicity intersections,
II. The deleted product criterion in the r-metastable range,” presented at the
SoCG: Symposium on Computational Geometry, Medford, MA, USA, 2016, vol. 51, p.
51.1-51.12.'
ista: 'Mabillard I, Wagner U. 2016. Eliminating higher-multiplicity intersections,
II. The deleted product criterion in the r-metastable range. SoCG: Symposium on
Computational Geometry, LIPIcs, vol. 51, 51.1-51.12.'
mla: Mabillard, Isaac, and Uli Wagner. Eliminating Higher-Multiplicity Intersections,
II. The Deleted Product Criterion in the r-Metastable Range. Vol. 51, Schloss
Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016, p. 51.1-51.12, doi:10.4230/LIPIcs.SoCG.2016.51.
short: I. Mabillard, U. Wagner, in:, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik
GmbH, 2016, p. 51.1-51.12.
conference:
end_date: 2016-06-17
location: Medford, MA, USA
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2016-06-14
date_created: 2018-12-11T11:51:41Z
date_published: 2016-06-01T00:00:00Z
date_updated: 2021-01-12T06:50:17Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2016.51
file:
- access_level: open_access
checksum: 92c0c3735fe908f8ded6e484005cb3b1
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:06Z
date_updated: 2020-07-14T12:44:47Z
file_id: '4791'
file_name: IST-2016-621-v1+1_LIPIcs-SoCG-2016-51.pdf
file_size: 622969
relation: main_file
file_date_updated: 2020-07-14T12:44:47Z
has_accepted_license: '1'
intvolume: ' 51'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 51.1 - 51.12
project:
- _id: 25FA3206-B435-11E9-9278-68D0E5697425
grant_number: PP00P2_138948
name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics'
publication_status: published
publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH
publist_id: '5830'
pubrep_id: '621'
quality_controlled: '1'
scopus_import: 1
status: public
title: Eliminating higher-multiplicity intersections, II. The deleted product criterion
in the r-metastable range
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: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2016'
...
---
_id: '1411'
abstract:
- lang: eng
text: We consider two systems (α1, …, αm) and (β1, …,βn) of simple curves drawn
on a compact two-dimensional surface M with boundary. Each αi and each βj is either
an arc meeting the boundary of M at its two endpoints, or a closed curve. The
αi are pairwise disjoint except for possibly sharing endpoints, and similarly
for the βj. We want to “untangle” the βj from the ai by a self-homeomorphism of
M; more precisely, we seek a homeomorphism φ:M→M fixing the boundary of M pointwise
such that the total number of crossings of the ai with the φ(βj) is as small as
possible. This problem is motivated by an application in the algorithmic theory
of embeddings and 3-manifolds. We prove that if M is planar, i.e., a sphere with
h ≥ 0 boundary components (“holes”), then O(mn) crossings can be achieved (independently
of h), which is asymptotically tight, as an easy lower bound shows. In general,
for an arbitrary (orientable or nonorientable) surface M with h holes and of (orientable
or nonorientable) genus g ≥ 0, we obtain an O((m + n)4) upper bound, again independent
of h and g. The proofs rely, among other things, on a result concerning simultaneous
planar drawings of graphs by Erten and Kobourov.
acknowledgement: 'Supported by the ERC Adv anced Grant No. 267165. '
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Eric
full_name: Sedgwick, Eric
last_name: Sedgwick
- first_name: Martin
full_name: Tancer, Martin
id: 38AC689C-F248-11E8-B48F-1D18A9856A87
last_name: Tancer
orcid: 0000-0002-1191-6714
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Matoušek J, Sedgwick E, Tancer M, Wagner U. Untangling two systems of noncrossing
curves. Israel Journal of Mathematics. 2016;212(1):37-79. doi:10.1007/s11856-016-1294-9
apa: Matoušek, J., Sedgwick, E., Tancer, M., & Wagner, U. (2016). Untangling
two systems of noncrossing curves. Israel Journal of Mathematics. Springer.
https://doi.org/10.1007/s11856-016-1294-9
chicago: Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Untangling
Two Systems of Noncrossing Curves.” Israel Journal of Mathematics. Springer,
2016. https://doi.org/10.1007/s11856-016-1294-9.
ieee: J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Untangling two systems
of noncrossing curves,” Israel Journal of Mathematics, vol. 212, no. 1.
Springer, pp. 37–79, 2016.
ista: Matoušek J, Sedgwick E, Tancer M, Wagner U. 2016. Untangling two systems of
noncrossing curves. Israel Journal of Mathematics. 212(1), 37–79.
mla: Matoušek, Jiří, et al. “Untangling Two Systems of Noncrossing Curves.” Israel
Journal of Mathematics, vol. 212, no. 1, Springer, 2016, pp. 37–79, doi:10.1007/s11856-016-1294-9.
short: J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, Israel Journal of Mathematics
212 (2016) 37–79.
date_created: 2018-12-11T11:51:52Z
date_published: 2016-05-01T00:00:00Z
date_updated: 2023-02-23T10:34:31Z
day: '01'
department:
- _id: UlWa
doi: 10.1007/s11856-016-1294-9
intvolume: ' 212'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1302.6475
month: '05'
oa: 1
oa_version: Preprint
page: 37 - 79
project:
- _id: 25FA3206-B435-11E9-9278-68D0E5697425
grant_number: PP00P2_138948
name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics'
publication: Israel Journal of Mathematics
publication_status: published
publisher: Springer
publist_id: '5796'
quality_controlled: '1'
related_material:
record:
- id: '2244'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Untangling two systems of noncrossing curves
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 212
year: '2016'
...
---
_id: '2154'
abstract:
- lang: eng
text: A result of Boros and Füredi (d = 2) and of Bárány (arbitrary d) asserts that
for every d there exists cd > 0 such that for every n-point set P ⊂ ℝd, some
point of ℝd is covered by at least (Formula presented.) of the d-simplices spanned
by the points of P. The largest possible value of cd has been the subject of ongoing
research. Recently Gromov improved the existing lower bounds considerably by introducing
a new, topological proof method. We provide an exposition of the combinatorial
component of Gromov's approach, in terms accessible to combinatorialists and discrete
geometers, and we investigate the limits of his method. In particular, we give
tighter bounds on the cofilling profiles for the (n - 1)-simplex. These bounds
yield a minor improvement over Gromov's lower bounds on cd for large d, but they
also show that the room for further improvement through the cofilling profiles
alone is quite small. We also prove a slightly better lower bound for c3 by an
approach using an additional structure besides the cofilling profiles. We formulate
a combinatorial extremal problem whose solution might perhaps lead to a tight
lower bound for cd.
acknowledgement: Swiss National Science Foundation (SNF 200021-125309, 200020-138230,
200020-12507)
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Matoušek J, Wagner U. On Gromov’s method of selecting heavily covered points.
Discrete & Computational Geometry. 2014;52(1):1-33. doi:10.1007/s00454-014-9584-7
apa: Matoušek, J., & Wagner, U. (2014). On Gromov’s method of selecting heavily
covered points. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-014-9584-7
chicago: Matoušek, Jiří, and Uli Wagner. “On Gromov’s Method of Selecting Heavily
Covered Points.” Discrete & Computational Geometry. Springer, 2014.
https://doi.org/10.1007/s00454-014-9584-7.
ieee: J. Matoušek and U. Wagner, “On Gromov’s method of selecting heavily covered
points,” Discrete & Computational Geometry, vol. 52, no. 1. Springer,
pp. 1–33, 2014.
ista: Matoušek J, Wagner U. 2014. On Gromov’s method of selecting heavily covered
points. Discrete & Computational Geometry. 52(1), 1–33.
mla: Matoušek, Jiří, and Uli Wagner. “On Gromov’s Method of Selecting Heavily Covered
Points.” Discrete & Computational Geometry, vol. 52, no. 1, Springer,
2014, pp. 1–33, doi:10.1007/s00454-014-9584-7.
short: J. Matoušek, U. Wagner, Discrete & Computational Geometry 52 (2014) 1–33.
date_created: 2018-12-11T11:56:01Z
date_published: 2014-07-01T00:00:00Z
date_updated: 2021-01-12T06:55:38Z
day: '01'
department:
- _id: UlWa
doi: 10.1007/s00454-014-9584-7
intvolume: ' 52'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1102.3515
month: '07'
oa: 1
oa_version: Submitted Version
page: 1 - 33
project:
- _id: 25FA3206-B435-11E9-9278-68D0E5697425
grant_number: PP00P2_138948
name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics'
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '4852'
quality_controlled: '1'
scopus_import: 1
status: public
title: On Gromov's method of selecting heavily covered points
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 52
year: '2014'
...
---
_id: '2244'
abstract:
- lang: eng
text: 'We consider two systems (α1,...,αm) and (β1,...,βn) of curves drawn on a
compact two-dimensional surface ℳ with boundary. Each αi and each βj is either
an arc meeting the boundary of ℳ at its two endpoints, or a closed curve. The
αi are pairwise disjoint except for possibly sharing endpoints, and similarly
for the βj. We want to "untangle" the βj from the αi by a self-homeomorphism
of ℳ; more precisely, we seek an homeomorphism φ: ℳ → ℳ fixing the boundary of
ℳ pointwise such that the total number of crossings of the αi with the φ(βj) is
as small as possible. This problem is motivated by an application in the algorithmic
theory of embeddings and 3-manifolds. We prove that if ℳ is planar, i.e., a sphere
with h ≥ 0 boundary components ("holes"), then O(mn) crossings can be
achieved (independently of h), which is asymptotically tight, as an easy lower
bound shows. In general, for an arbitrary (orientable or nonorientable) surface
ℳ with h holes and of (orientable or nonorientable) genus g ≥ 0, we obtain an
O((m + n)4) upper bound, again independent of h and g. '
acknowledgement: We would like to thank the authors of [GHR13] for mak- ing a draft
of their paper available to us, and, in particular, T. Huynh for an e-mail correspondence.
alternative_title:
- LNCS
arxiv: 1
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Eric
full_name: Sedgwick, Eric
last_name: Sedgwick
- first_name: Martin
full_name: Tancer, Martin
id: 38AC689C-F248-11E8-B48F-1D18A9856A87
last_name: Tancer
orcid: 0000-0002-1191-6714
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: Matoušek J, Sedgwick E, Tancer M, Wagner U. Untangling two systems of noncrossing
curves. 2013;8242:472-483. doi:10.1007/978-3-319-03841-4_41
apa: 'Matoušek, J., Sedgwick, E., Tancer, M., & Wagner, U. (2013). Untangling
two systems of noncrossing curves. Presented at the GD: Graph Drawing and Network
Visualization, Bordeaux, France: Springer. https://doi.org/10.1007/978-3-319-03841-4_41'
chicago: Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Untangling
Two Systems of Noncrossing Curves.” Lecture Notes in Computer Science. Springer,
2013. https://doi.org/10.1007/978-3-319-03841-4_41.
ieee: J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Untangling two systems
of noncrossing curves,” vol. 8242. Springer, pp. 472–483, 2013.
ista: Matoušek J, Sedgwick E, Tancer M, Wagner U. 2013. Untangling two systems of
noncrossing curves. 8242, 472–483.
mla: Matoušek, Jiří, et al. Untangling Two Systems of Noncrossing Curves.
Vol. 8242, Springer, 2013, pp. 472–83, doi:10.1007/978-3-319-03841-4_41.
short: J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, 8242 (2013) 472–483.
conference:
end_date: 2013-09-25
location: Bordeaux, France
name: 'GD: Graph Drawing and Network Visualization'
start_date: 2013-09-23
date_created: 2018-12-11T11:56:32Z
date_published: 2013-09-01T00:00:00Z
date_updated: 2023-02-21T17:03:07Z
day: '01'
department:
- _id: UlWa
doi: 10.1007/978-3-319-03841-4_41
external_id:
arxiv:
- '1302.6475'
intvolume: ' 8242'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1302.6475
month: '09'
oa: 1
oa_version: Preprint
page: 472 - 483
project:
- _id: 25FA3206-B435-11E9-9278-68D0E5697425
grant_number: PP00P2_138948
name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics'
publication_status: published
publisher: Springer
publist_id: '4707'
quality_controlled: '1'
related_material:
record:
- id: '1411'
relation: later_version
status: public
scopus_import: 1
series_title: Lecture Notes in Computer Science
status: public
title: Untangling two systems of noncrossing curves
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8242
year: '2013'
...