---
_id: '13042'
abstract:
- lang: eng
  text: Let Lc,n denote the size of the longest cycle in G(n, c/n),c >1 constant.  We
    show that there exists a continuous function f(c) such that Lc,n/n→f(c) a.s.  for
    c>20,  thus  extending  a  result  of  Frieze  and  the  author  to  smaller  values  of
    c. Thereafter,  for c>20,  we  determine  the  limit  of  the  probability  that
    G(n, c/n)contains  cycles  of  every  length  between  the  length  of  its  shortest  and  its  longest
    cycles as n→∞.
acknowledgement: We would like to thank the reviewers for their helpful comments and
  remarks.
article_number: P2.21
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Michael
  full_name: Anastos, Michael
  id: 0b2a4358-bb35-11ec-b7b9-e3279b593dbb
  last_name: Anastos
citation:
  ama: Anastos M. A note on long cycles in sparse random graphs. <i>Electronic Journal
    of Combinatorics</i>. 2023;30(2). doi:<a href="https://doi.org/10.37236/11471">10.37236/11471</a>
  apa: Anastos, M. (2023). A note on long cycles in sparse random graphs. <i>Electronic
    Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href="https://doi.org/10.37236/11471">https://doi.org/10.37236/11471</a>
  chicago: Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” <i>Electronic
    Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2023. <a href="https://doi.org/10.37236/11471">https://doi.org/10.37236/11471</a>.
  ieee: M. Anastos, “A note on long cycles in sparse random graphs,” <i>Electronic
    Journal of Combinatorics</i>, vol. 30, no. 2. Electronic Journal of Combinatorics,
    2023.
  ista: Anastos M. 2023. A note on long cycles in sparse random graphs. Electronic
    Journal of Combinatorics. 30(2), P2.21.
  mla: Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” <i>Electronic
    Journal of Combinatorics</i>, vol. 30, no. 2, P2.21, Electronic Journal of Combinatorics,
    2023, doi:<a href="https://doi.org/10.37236/11471">10.37236/11471</a>.
  short: M. Anastos, Electronic Journal of Combinatorics 30 (2023).
date_created: 2023-05-21T22:01:05Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2023-08-01T14:44:52Z
day: '05'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.37236/11471
external_id:
  arxiv:
  - '2105.13828'
  isi:
  - '000988285500001'
file:
- access_level: open_access
  checksum: 6269ed3b3eded6536d3d9d6baad2d5b9
  content_type: application/pdf
  creator: dernst
  date_created: 2023-05-22T07:43:19Z
  date_updated: 2023-05-22T07:43:19Z
  file_id: '13046'
  file_name: 2023_JourCombinatorics_Anastos.pdf
  file_size: 448736
  relation: main_file
  success: 1
file_date_updated: 2023-05-22T07:43:19Z
has_accepted_license: '1'
intvolume: '        30'
isi: 1
issue: '2'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
publication: Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A note on long cycles in sparse random graphs
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: 30
year: '2023'
...
---
_id: '14319'
abstract:
- lang: eng
  text: "We study multigraphs whose edge-sets are the union of three perfect matchings,
    M1, M2, and M3. Given such a graph G and any a1; a2; a3 2 N with a1 +a2 +a3 6
    n - 2, we show there exists a matching M of G with jM \\ Mij = ai for each i 2
    f1; 2; 3g. The bound n - 2 in the theorem is best possible in general. We conjecture
    however that if G is bipartite, the same result holds with n - 2 replaced by n
    - 1. We give a construction that shows such a result would be tight. We\r\nalso
    make a conjecture generalising the Ryser-Brualdi-Stein conjecture with colour\r\nmultiplicities."
acknowledgement: Anastos has received funding from the European Union’s Horizon 2020
  research and in-novation programme under the Marie Sk lodowska-Curie grant agreement
  No 101034413.Fabian’s research is supported by the Deutsche Forschungsgemeinschaft
  (DFG, GermanResearch Foundation) Graduiertenkolleg “Facets of Complexity” (GRK 2434).
article_number: P3.10
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Michael
  full_name: Anastos, Michael
  id: 0b2a4358-bb35-11ec-b7b9-e3279b593dbb
  last_name: Anastos
- first_name: David
  full_name: Fabian, David
  last_name: Fabian
- first_name: Alp
  full_name: Müyesser, Alp
  last_name: Müyesser
- first_name: Tibor
  full_name: Szabó, Tibor
  last_name: Szabó
citation:
  ama: Anastos M, Fabian D, Müyesser A, Szabó T. Splitting matchings and the Ryser-Brualdi-Stein
    conjecture for multisets. <i>Electronic Journal of Combinatorics</i>. 2023;30(3).
    doi:<a href="https://doi.org/10.37236/11714">10.37236/11714</a>
  apa: Anastos, M., Fabian, D., Müyesser, A., &#38; Szabó, T. (2023). Splitting matchings
    and the Ryser-Brualdi-Stein conjecture for multisets. <i>Electronic Journal of
    Combinatorics</i>. Electronic Journal of Combinatorics. <a href="https://doi.org/10.37236/11714">https://doi.org/10.37236/11714</a>
  chicago: Anastos, Michael, David Fabian, Alp Müyesser, and Tibor Szabó. “Splitting
    Matchings and the Ryser-Brualdi-Stein Conjecture for Multisets.” <i>Electronic
    Journal of Combinatorics</i>. Electronic Journal of Combinatorics, 2023. <a href="https://doi.org/10.37236/11714">https://doi.org/10.37236/11714</a>.
  ieee: M. Anastos, D. Fabian, A. Müyesser, and T. Szabó, “Splitting matchings and
    the Ryser-Brualdi-Stein conjecture for multisets,” <i>Electronic Journal of Combinatorics</i>,
    vol. 30, no. 3. Electronic Journal of Combinatorics, 2023.
  ista: Anastos M, Fabian D, Müyesser A, Szabó T. 2023. Splitting matchings and the
    Ryser-Brualdi-Stein conjecture for multisets. Electronic Journal of Combinatorics.
    30(3), P3.10.
  mla: Anastos, Michael, et al. “Splitting Matchings and the Ryser-Brualdi-Stein Conjecture
    for Multisets.” <i>Electronic Journal of Combinatorics</i>, vol. 30, no. 3, P3.10,
    Electronic Journal of Combinatorics, 2023, doi:<a href="https://doi.org/10.37236/11714">10.37236/11714</a>.
  short: M. Anastos, D. Fabian, A. Müyesser, T. Szabó, Electronic Journal of Combinatorics
    30 (2023).
date_created: 2023-09-10T22:01:12Z
date_published: 2023-07-28T00:00:00Z
date_updated: 2023-09-15T08:12:30Z
day: '28'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.37236/11714
ec_funded: 1
external_id:
  arxiv:
  - '2212.03100'
file:
- access_level: open_access
  checksum: 52c46c8cb329f9aaee9ade01525f317b
  content_type: application/pdf
  creator: dernst
  date_created: 2023-09-15T08:02:09Z
  date_updated: 2023-09-15T08:02:09Z
  file_id: '14338'
  file_name: 2023_elecJournCombinatorics_Anastos.pdf
  file_size: 247917
  relation: main_file
  success: 1
file_date_updated: 2023-09-15T08:02:09Z
has_accepted_license: '1'
intvolume: '        30'
issue: '3'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Splitting matchings and the Ryser-Brualdi-Stein conjecture for multisets
tmp:
  image: /image/cc_by_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
  name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
  short: CC BY-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2023'
...
---
_id: '12286'
abstract:
- lang: eng
  text: "Inspired by the study of loose cycles in hypergraphs, we define the loose
    core in hypergraphs as a structurewhich mirrors the close relationship between
    cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial random
    hypergraph $H^r(n,p)$, the order of the loose core undergoes a phase transition
    at a certain critical threshold and determine this order, as well as the number
    of edges, asymptotically in the subcritical and supercritical regimes.&#x0D;\r\nOur
    main tool is an algorithm called CoreConstruct, which enables us to analyse a
    peeling process for the loose core. By analysing this algorithm we determine the
    asymptotic degree distribution of vertices in the loose core and in particular
    how many vertices and edges the loose core contains. As a corollary we obtain
    an improved upper bound on the length of the longest loose cycle in $H^r(n,p)$."
acknowledgement: 'Supported by Austrian Science Fund (FWF): I3747, W1230.'
article_number: P4.13
article_processing_charge: No
article_type: original
author:
- first_name: Oliver
  full_name: Cooley, Oliver
  id: 43f4ddd0-a46b-11ec-8df6-ef3703bd721d
  last_name: Cooley
- first_name: Mihyun
  full_name: Kang, Mihyun
  last_name: Kang
- first_name: Julian
  full_name: Zalla, Julian
  last_name: Zalla
citation:
  ama: Cooley O, Kang M, Zalla J. Loose cores and cycles in random hypergraphs. <i>The
    Electronic Journal of Combinatorics</i>. 2022;29(4). doi:<a href="https://doi.org/10.37236/10794">10.37236/10794</a>
  apa: Cooley, O., Kang, M., &#38; Zalla, J. (2022). Loose cores and cycles in random
    hypergraphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal
    of Combinatorics. <a href="https://doi.org/10.37236/10794">https://doi.org/10.37236/10794</a>
  chicago: Cooley, Oliver, Mihyun Kang, and Julian Zalla. “Loose Cores and Cycles
    in Random Hypergraphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic
    Journal of Combinatorics, 2022. <a href="https://doi.org/10.37236/10794">https://doi.org/10.37236/10794</a>.
  ieee: O. Cooley, M. Kang, and J. Zalla, “Loose cores and cycles in random hypergraphs,”
    <i>The Electronic Journal of Combinatorics</i>, vol. 29, no. 4. The Electronic
    Journal of Combinatorics, 2022.
  ista: Cooley O, Kang M, Zalla J. 2022. Loose cores and cycles in random hypergraphs.
    The Electronic Journal of Combinatorics. 29(4), P4.13.
  mla: Cooley, Oliver, et al. “Loose Cores and Cycles in Random Hypergraphs.” <i>The
    Electronic Journal of Combinatorics</i>, vol. 29, no. 4, P4.13, The Electronic
    Journal of Combinatorics, 2022, doi:<a href="https://doi.org/10.37236/10794">10.37236/10794</a>.
  short: O. Cooley, M. Kang, J. Zalla, The Electronic Journal of Combinatorics 29
    (2022).
date_created: 2023-01-16T10:03:57Z
date_published: 2022-10-21T00:00:00Z
date_updated: 2023-08-04T10:29:18Z
day: '21'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.37236/10794
external_id:
  isi:
  - '000876763300001'
file:
- access_level: open_access
  checksum: 00122b2459f09b5ae43073bfba565e94
  content_type: application/pdf
  creator: dernst
  date_created: 2023-01-30T11:45:13Z
  date_updated: 2023-01-30T11:45:13Z
  file_id: '12462'
  file_name: 2022_ElecJournCombinatorics_Cooley_Kang_Zalla.pdf
  file_size: 626953
  relation: main_file
  success: 1
file_date_updated: 2023-01-30T11:45:13Z
has_accepted_license: '1'
intvolume: '        29'
isi: 1
issue: '4'
keyword:
- Computational Theory and Mathematics
- Geometry and Topology
- Theoretical Computer Science
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
publication: The Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: The Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Loose cores and cycles in random hypergraphs
tmp:
  image: /image/cc_by_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
  name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
  short: CC BY-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 29
year: '2022'
...
---
_id: '11740'
abstract:
- lang: eng
  text: "We consider a generalised model of a random simplicial complex, which arises
    from a random hypergraph. Our model is generated by taking the downward-closure
    of a non-uniform binomial random hypergraph, in which for each k, each set of
    k+1 vertices forms an edge with some probability pk independently. As a special
    case, this contains an extensively studied model of a (uniform) random simplicial
    complex, introduced by Meshulam and Wallach [Random Structures & Algorithms 34
    (2009), no. 3, pp. 408–417].\r\nWe consider a higher-dimensional notion of connectedness
    on this new model according to the vanishing of cohomology groups over an arbitrary
    abelian group R. We prove that this notion of connectedness displays a phase transition
    and determine the threshold. We also prove a hitting time result for a natural
    process interpretation, in which simplices and their downward-closure are added
    one by one. In addition, we determine the asymptotic behaviour of cohomology groups
    inside the critical window around the time of the phase transition."
acknowledgement: 'Supported by Austrian Science Fund (FWF): I3747, W1230.'
article_number: P3.27
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Oliver
  full_name: Cooley, Oliver
  id: 43f4ddd0-a46b-11ec-8df6-ef3703bd721d
  last_name: Cooley
- first_name: Nicola
  full_name: Del Giudice, Nicola
  last_name: Del Giudice
- first_name: Mihyun
  full_name: Kang, Mihyun
  last_name: Kang
- first_name: Philipp
  full_name: Sprüssel, Philipp
  last_name: Sprüssel
citation:
  ama: Cooley O, Del Giudice N, Kang M, Sprüssel P. Phase transition in cohomology
    groups of non-uniform random simplicial complexes. <i>Electronic Journal of Combinatorics</i>.
    2022;29(3). doi:<a href="https://doi.org/10.37236/10607">10.37236/10607</a>
  apa: Cooley, O., Del Giudice, N., Kang, M., &#38; Sprüssel, P. (2022). Phase transition
    in cohomology groups of non-uniform random simplicial complexes. <i>Electronic
    Journal of Combinatorics</i>. Electronic Journal of Combinatorics. <a href="https://doi.org/10.37236/10607">https://doi.org/10.37236/10607</a>
  chicago: Cooley, Oliver, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel.
    “Phase Transition in Cohomology Groups of Non-Uniform Random Simplicial Complexes.”
    <i>Electronic Journal of Combinatorics</i>. Electronic Journal of Combinatorics,
    2022. <a href="https://doi.org/10.37236/10607">https://doi.org/10.37236/10607</a>.
  ieee: O. Cooley, N. Del Giudice, M. Kang, and P. Sprüssel, “Phase transition in
    cohomology groups of non-uniform random simplicial complexes,” <i>Electronic Journal
    of Combinatorics</i>, vol. 29, no. 3. Electronic Journal of Combinatorics, 2022.
  ista: Cooley O, Del Giudice N, Kang M, Sprüssel P. 2022. Phase transition in cohomology
    groups of non-uniform random simplicial complexes. Electronic Journal of Combinatorics.
    29(3), P3.27.
  mla: Cooley, Oliver, et al. “Phase Transition in Cohomology Groups of Non-Uniform
    Random Simplicial Complexes.” <i>Electronic Journal of Combinatorics</i>, vol.
    29, no. 3, P3.27, Electronic Journal of Combinatorics, 2022, doi:<a href="https://doi.org/10.37236/10607">10.37236/10607</a>.
  short: O. Cooley, N. Del Giudice, M. Kang, P. Sprüssel, Electronic Journal of Combinatorics
    29 (2022).
date_created: 2022-08-07T22:01:59Z
date_published: 2022-07-29T00:00:00Z
date_updated: 2023-08-03T12:37:54Z
day: '29'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.37236/10607
external_id:
  arxiv:
  - '2005.07103'
  isi:
  - '000836200300001'
file:
- access_level: open_access
  checksum: 057c676dcee70236aa234d4ce6138c69
  content_type: application/pdf
  creator: dernst
  date_created: 2022-08-08T06:28:52Z
  date_updated: 2022-08-08T06:28:52Z
  file_id: '11742'
  file_name: 2022_ElecJournCombinatorics_Cooley.pdf
  file_size: 1768663
  relation: main_file
  success: 1
file_date_updated: 2022-08-08T06:28:52Z
has_accepted_license: '1'
intvolume: '        29'
isi: 1
issue: '3'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Phase transition in cohomology groups of non-uniform random simplicial complexes
tmp:
  image: /image/cc_by_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
  name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
  short: CC BY-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 29
year: '2022'
...
---
_id: '1642'
abstract:
- lang: eng
  text: The Hanani-Tutte theorem is a classical result proved for the first time in
    the 1930s that characterizes planar graphs as graphs that admit a drawing in the
    plane in which every pair of edges not sharing a vertex cross an even number of
    times. We generalize this result to clustered graphs with two disjoint clusters,
    and show that a straightforward extension to flat clustered graphs with three
    or more disjoint clusters is not possible. For general clustered graphs we show
    a variant of the Hanani-Tutte theorem in the case when each cluster induces a
    connected subgraph. Di Battista and Frati proved that clustered planarity of embedded
    clustered graphs whose every face is incident to at most five vertices can be
    tested in polynomial time. We give a new and short proof of this result, using
    the matroid intersection algorithm.
acknowledgement: e research leading to these results has received funding fromthe
  People Programme (Marie Curie Actions) of the European Union’s Seventh Framework
  Programme(FP7/2007-2013) under REA grant agreement no [291734], and ESF Eurogiga
  project GraDR as GAˇCRGIG/11/E023.
article_number: 'P4.24 '
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
- first_name: Igor
  full_name: Malinovič, Igor
  last_name: Malinovič
- first_name: Dömötör
  full_name: Pálvölgyi, Dömötör
  last_name: Pálvölgyi
citation:
  ama: Fulek R, Kynčl J, Malinovič I, Pálvölgyi D. Clustered planarity testing revisited.
    <i>Electronic Journal of Combinatorics</i>. 2015;22(4). doi:<a href="https://doi.org/10.37236/5002">10.37236/5002</a>
  apa: Fulek, R., Kynčl, J., Malinovič, I., &#38; Pálvölgyi, D. (2015). Clustered
    planarity testing revisited. <i>Electronic Journal of Combinatorics</i>. Electronic
    Journal of Combinatorics. <a href="https://doi.org/10.37236/5002">https://doi.org/10.37236/5002</a>
  chicago: Fulek, Radoslav, Jan Kynčl, Igor Malinovič, and Dömötör Pálvölgyi. “Clustered
    Planarity Testing Revisited.” <i>Electronic Journal of Combinatorics</i>. Electronic
    Journal of Combinatorics, 2015. <a href="https://doi.org/10.37236/5002">https://doi.org/10.37236/5002</a>.
  ieee: R. Fulek, J. Kynčl, I. Malinovič, and D. Pálvölgyi, “Clustered planarity testing
    revisited,” <i>Electronic Journal of Combinatorics</i>, vol. 22, no. 4. Electronic
    Journal of Combinatorics, 2015.
  ista: Fulek R, Kynčl J, Malinovič I, Pálvölgyi D. 2015. Clustered planarity testing
    revisited. Electronic Journal of Combinatorics. 22(4), P4.24.
  mla: Fulek, Radoslav, et al. “Clustered Planarity Testing Revisited.” <i>Electronic
    Journal of Combinatorics</i>, vol. 22, no. 4, P4.24, Electronic Journal of Combinatorics,
    2015, doi:<a href="https://doi.org/10.37236/5002">10.37236/5002</a>.
  short: R. Fulek, J. Kynčl, I. Malinovič, D. Pálvölgyi, Electronic Journal of Combinatorics
    22 (2015).
date_created: 2018-12-11T11:53:12Z
date_published: 2015-11-13T00:00:00Z
date_updated: 2023-02-21T16:03:02Z
day: '13'
ddc:
- '514'
- '516'
department:
- _id: UlWa
doi: 10.37236/5002
ec_funded: 1
external_id:
  arxiv:
  - '1305.4519'
file:
- access_level: open_access
  checksum: 40b5920b49ee736694f59f39588ee206
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:15:03Z
  date_updated: 2020-07-14T12:45:08Z
  file_id: '5120'
  file_name: IST-2016-714-v1+1_5002-15499-3-PB.pdf
  file_size: 443655
  relation: main_file
file_date_updated: 2020-07-14T12:45:08Z
has_accepted_license: '1'
intvolume: '        22'
issue: '4'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: Electronic Journal of Combinatorics
publist_id: '5511'
pubrep_id: '714'
quality_controlled: '1'
related_material:
  record:
  - id: '10793'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: Clustered planarity testing revisited
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2015'
...
---
_id: '9594'
abstract:
- lang: eng
  text: Let d≥3 be a fixed integer. We give an asympotic formula for the expected
    number of spanning trees in a uniformly random d-regular graph with n vertices.
    (The asymptotics are as n→∞, restricted to even n if d is odd.) We also obtain
    the asymptotic distribution of the number of spanning trees in a uniformly random
    cubic graph, and conjecture that the corresponding result holds for arbitrary
    (fixed) d. Numerical evidence is presented which supports our conjecture.
article_number: P1.45
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Catherine
  full_name: Greenhill, Catherine
  last_name: Greenhill
- first_name: Matthew Alan
  full_name: Kwan, Matthew Alan
  id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
  last_name: Kwan
  orcid: 0000-0002-4003-7567
- first_name: David
  full_name: Wind, David
  last_name: Wind
citation:
  ama: Greenhill C, Kwan MA, Wind D. On the number of spanning trees in random regular
    graphs. <i>The Electronic Journal of Combinatorics</i>. 2014;21(1). doi:<a href="https://doi.org/10.37236/3752">10.37236/3752</a>
  apa: Greenhill, C., Kwan, M. A., &#38; Wind, D. (2014). On the number of spanning
    trees in random regular graphs. <i>The Electronic Journal of Combinatorics</i>.
    The Electronic Journal of Combinatorics. <a href="https://doi.org/10.37236/3752">https://doi.org/10.37236/3752</a>
  chicago: Greenhill, Catherine, Matthew Alan Kwan, and David Wind. “On the Number
    of Spanning Trees in Random Regular Graphs.” <i>The Electronic Journal of Combinatorics</i>.
    The Electronic Journal of Combinatorics, 2014. <a href="https://doi.org/10.37236/3752">https://doi.org/10.37236/3752</a>.
  ieee: C. Greenhill, M. A. Kwan, and D. Wind, “On the number of spanning trees in
    random regular graphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 21,
    no. 1. The Electronic Journal of Combinatorics, 2014.
  ista: Greenhill C, Kwan MA, Wind D. 2014. On the number of spanning trees in random
    regular graphs. The Electronic Journal of Combinatorics. 21(1), P1.45.
  mla: Greenhill, Catherine, et al. “On the Number of Spanning Trees in Random Regular
    Graphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 21, no. 1, P1.45,
    The Electronic Journal of Combinatorics, 2014, doi:<a href="https://doi.org/10.37236/3752">10.37236/3752</a>.
  short: C. Greenhill, M.A. Kwan, D. Wind, The Electronic Journal of Combinatorics
    21 (2014).
date_created: 2021-06-23T06:29:35Z
date_published: 2014-02-28T00:00:00Z
date_updated: 2023-02-23T14:02:12Z
day: '28'
doi: 10.37236/3752
extern: '1'
external_id:
  arxiv:
  - '1309.6710'
intvolume: '        21'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.37236/3752
month: '02'
oa: 1
oa_version: Published Version
publication: The Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: The Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the number of spanning trees in random regular graphs
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 21
year: '2014'
...
