---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21159'
abstract:
- lang: eng
text: "One of the foundational theorems of extremal graph theory is Dirac’s theorem,
which\r\nsays that if an n-vertex graph G has minimum degree at least n/2, then
G has a\r\nHamilton cycle, and therefore a perfect matching (if n is even). Later
work by Sárközy,\r\nSelkow and Szemerédi showed that in fact Dirac graphs have
many Hamilton cycles\r\nand perfect matchings, culminating in a result of Cuckler
and Kahn that gives a precise\r\ndescription of the numbers of Hamilton cycles
and perfect matchings in a Dirac graph\r\nG (in terms of an entropy-like parameter
of G). In this paper we extend Cuckler\r\nand Kahn’s result to perfect matchings
in hypergraphs. For positive integers d < k,\r\nand for n divisible by k, let
md (k, n) be the minimum d-degree that ensures the\r\nexistence of a perfect matching
in an n-vertex k-uniform hypergraph. In general, it is\r\nan open question to
determine (even asymptotically) the values of md (k, n), but we are\r\nnonetheless
able to prove an analogue of the Cuckler–Kahn theorem, showing that if\r\nan n-vertex
k-uniform hypergraph G has minimum d-degree at least (1+γ )md (k, n)\r\n(for any
constantγ > 0), then the number of perfect matchings in G is controlled by\r\nan
entropy-like parameter of G. This strengthens cruder estimates arising from work\r\nof
Kang–Kelly–Kühn–Osthus–Pfenninger and Pham–Sah–Sawhney–Simkin."
acknowledgement: We would like to thank the referees for a number of helpful comments
and suggestions, which have substantially improved the paper. Open access funding
provided by Institute of Science and Technology (IST Austria).
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- 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: Roodabeh
full_name: Safavi Hemami, Roodabeh
id: 72ed2640-8972-11ed-ae7b-f9c81ec75154
last_name: Safavi Hemami
- first_name: Yiting
full_name: Wang, Yiting
id: 1917d194-076e-11ed-97cd-837255f88785
last_name: Wang
orcid: 0000-0002-2856-767X
citation:
ama: Kwan MA, Safavi Hemami R, Wang Y. Counting perfect matchings in Dirac hypergraphs.
Combinatorica. 2026;46. doi:10.1007/s00493-025-00194-8
apa: Kwan, M. A., Safavi Hemami, R., & Wang, Y. (2026). Counting perfect matchings
in Dirac hypergraphs. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-025-00194-8
chicago: Kwan, Matthew Alan, Roodabeh Safavi Hemami, and Yiting Wang. “Counting
Perfect Matchings in Dirac Hypergraphs.” Combinatorica. Springer Nature,
2026. https://doi.org/10.1007/s00493-025-00194-8.
ieee: M. A. Kwan, R. Safavi Hemami, and Y. Wang, “Counting perfect matchings in
Dirac hypergraphs,” Combinatorica, vol. 46. Springer Nature, 2026.
ista: Kwan MA, Safavi Hemami R, Wang Y. 2026. Counting perfect matchings in Dirac
hypergraphs. Combinatorica. 46, 5.
mla: Kwan, Matthew Alan, et al. “Counting Perfect Matchings in Dirac Hypergraphs.”
Combinatorica, vol. 46, 5, Springer Nature, 2026, doi:10.1007/s00493-025-00194-8.
short: M.A. Kwan, R. Safavi Hemami, Y. Wang, Combinatorica 46 (2026).
corr_author: '1'
date_created: 2026-02-08T23:02:49Z
date_published: 2026-02-01T00:00:00Z
date_updated: 2026-02-16T09:55:17Z
day: '01'
ddc:
- '510'
department:
- _id: MaKw
- _id: MoHe
doi: 10.1007/s00493-025-00194-8
external_id:
arxiv:
- '2408.09589'
file:
- access_level: open_access
checksum: 47b0031d90b0e6b9a843f422a1486089
content_type: application/pdf
creator: dernst
date_created: 2026-02-16T09:52:38Z
date_updated: 2026-02-16T09:52:38Z
file_id: '21228'
file_name: 2026_Combinatorica_Kwan.pdf
file_size: 539646
relation: main_file
success: 1
file_date_updated: 2026-02-16T09:52:38Z
has_accepted_license: '1'
intvolume: ' 46'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '02'
oa: 1
oa_version: Published Version
publication: Combinatorica
publication_identifier:
eissn:
- 1439-6912
issn:
- 0209-9683
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counting perfect matchings in Dirac hypergraphs
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: 46
year: '2026'
...
---
_id: '15275'
abstract:
- lang: eng
text: In 1916, Schur introduced the Ramsey number r(3; m), which is the minimum
integer n > 1 such that for any m-coloring of the edges of the complete graph
Kn, there is a monochromatic copy of K3. He showed that r(3; m) ≤ O(m!), and a
simple construction demonstrates that r(3; m) ≥ 2Ω(m). An old conjecture of Erdős
states that r(3; m) = 2Θ(m). In this note, we prove the conjecture for m-colorings
with bounded VC-dimension, that is, for m-colorings with the property that the
set system induced by the neighborhoods of the vertices with respect to each color
class has bounded VC-dimension.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jacob
full_name: Fox, Jacob
last_name: Fox
- first_name: János
full_name: Pach, János
id: E62E3130-B088-11EA-B919-BF823C25FEA4
last_name: Pach
- first_name: Andrew
full_name: Suk, Andrew
last_name: Suk
citation:
ama: Fox J, Pach J, Suk A. Bounded VC-dimension implies the Schur-Erdős conjecture.
Combinatorica. 2021;41(6):803-813. doi:10.1007/s00493-021-4530-9
apa: Fox, J., Pach, J., & Suk, A. (2021). Bounded VC-dimension implies the Schur-Erdős
conjecture. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-021-4530-9
chicago: Fox, Jacob, János Pach, and Andrew Suk. “Bounded VC-Dimension Implies the
Schur-Erdős Conjecture.” Combinatorica. Springer Nature, 2021. https://doi.org/10.1007/s00493-021-4530-9.
ieee: J. Fox, J. Pach, and A. Suk, “Bounded VC-dimension implies the Schur-Erdős
conjecture,” Combinatorica, vol. 41, no. 6. Springer Nature, pp. 803–813,
2021.
ista: Fox J, Pach J, Suk A. 2021. Bounded VC-dimension implies the Schur-Erdős conjecture.
Combinatorica. 41(6), 803–813.
mla: Fox, Jacob, et al. “Bounded VC-Dimension Implies the Schur-Erdős Conjecture.”
Combinatorica, vol. 41, no. 6, Springer Nature, 2021, pp. 803–13, doi:10.1007/s00493-021-4530-9.
short: J. Fox, J. Pach, A. Suk, Combinatorica 41 (2021) 803–813.
date_created: 2024-04-03T07:59:57Z
date_published: 2021-11-20T00:00:00Z
date_updated: 2024-04-09T10:40:08Z
day: '20'
department:
- _id: HeEd
doi: 10.1007/s00493-021-4530-9
external_id:
arxiv:
- '1912.02342'
intvolume: ' 41'
issue: '6'
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1912.02342
month: '11'
oa: 1
oa_version: Preprint
page: 803-813
publication: Combinatorica
publication_identifier:
eissn:
- 1439-6912
issn:
- 0209-9683
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Bounded VC-dimension implies the Schur-Erdős conjecture
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 41
year: '2021'
...
---
_id: '9582'
abstract:
- lang: eng
text: The problem of finding dense induced bipartite subgraphs in H-free graphs
has a long history, and was posed 30 years ago by Erdős, Faudree, Pach and Spencer.
In this paper, we obtain several results in this direction. First we prove that
any H-free graph with minimum degree at least d contains an induced bipartite
subgraph of minimum degree at least cH log d/log log d, thus nearly confirming
one and proving another conjecture of Esperet, Kang and Thomassé. Complementing
this result, we further obtain optimal bounds for this problem in the case of
dense triangle-free graphs, and we also answer a question of Erdœs, Janson, Łuczak
and Spencer.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- 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: Shoham
full_name: Letzter, Shoham
last_name: Letzter
- first_name: Benny
full_name: Sudakov, Benny
last_name: Sudakov
- first_name: Tuan
full_name: Tran, Tuan
last_name: Tran
citation:
ama: Kwan MA, Letzter S, Sudakov B, Tran T. Dense induced bipartite subgraphs in
triangle-free graphs. Combinatorica. 2020;40(2):283-305. doi:10.1007/s00493-019-4086-0
apa: Kwan, M. A., Letzter, S., Sudakov, B., & Tran, T. (2020). Dense induced
bipartite subgraphs in triangle-free graphs. Combinatorica. Springer. https://doi.org/10.1007/s00493-019-4086-0
chicago: Kwan, Matthew Alan, Shoham Letzter, Benny Sudakov, and Tuan Tran. “Dense
Induced Bipartite Subgraphs in Triangle-Free Graphs.” Combinatorica. Springer,
2020. https://doi.org/10.1007/s00493-019-4086-0.
ieee: M. A. Kwan, S. Letzter, B. Sudakov, and T. Tran, “Dense induced bipartite
subgraphs in triangle-free graphs,” Combinatorica, vol. 40, no. 2. Springer,
pp. 283–305, 2020.
ista: Kwan MA, Letzter S, Sudakov B, Tran T. 2020. Dense induced bipartite subgraphs
in triangle-free graphs. Combinatorica. 40(2), 283–305.
mla: Kwan, Matthew Alan, et al. “Dense Induced Bipartite Subgraphs in Triangle-Free
Graphs.” Combinatorica, vol. 40, no. 2, Springer, 2020, pp. 283–305, doi:10.1007/s00493-019-4086-0.
short: M.A. Kwan, S. Letzter, B. Sudakov, T. Tran, Combinatorica 40 (2020) 283–305.
date_created: 2021-06-22T06:42:26Z
date_published: 2020-04-01T00:00:00Z
date_updated: 2023-02-23T14:01:45Z
day: '01'
doi: 10.1007/s00493-019-4086-0
extern: '1'
external_id:
arxiv:
- '1810.12144'
intvolume: ' 40'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1810.12144
month: '04'
oa: 1
oa_version: Preprint
page: 283-305
publication: Combinatorica
publication_identifier:
eissn:
- 1439-6912
issn:
- 0209-9683
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dense induced bipartite subgraphs in triangle-free graphs
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 40
year: '2020'
...
---
_id: '7034'
abstract:
- lang: eng
text: We find a graph of genus 5 and its drawing on the orientable surface of genus
4 with every pair of independent edges crossing an even number of times. This
shows that the strong Hanani–Tutte theorem cannot be extended to the orientable
surface of genus 4. As a base step in the construction we use a counterexample
to an extension of the unified Hanani–Tutte theorem on the torus.
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. Counterexample to an extension of the Hanani-Tutte theorem
on the surface of genus 4. Combinatorica. 2019;39(6):1267-1279. doi:10.1007/s00493-019-3905-7
apa: Fulek, R., & Kynčl, J. (2019). Counterexample to an extension of the Hanani-Tutte
theorem on the surface of genus 4. Combinatorica. Springer Nature. https://doi.org/10.1007/s00493-019-3905-7
chicago: Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the
Hanani-Tutte Theorem on the Surface of Genus 4.” Combinatorica. Springer
Nature, 2019. https://doi.org/10.1007/s00493-019-3905-7.
ieee: R. Fulek and J. Kynčl, “Counterexample to an extension of the Hanani-Tutte
theorem on the surface of genus 4,” Combinatorica, vol. 39, no. 6. Springer
Nature, pp. 1267–1279, 2019.
ista: Fulek R, Kynčl J. 2019. Counterexample to an extension of the Hanani-Tutte
theorem on the surface of genus 4. Combinatorica. 39(6), 1267–1279.
mla: Fulek, Radoslav, and Jan Kynčl. “Counterexample to an Extension of the Hanani-Tutte
Theorem on the Surface of Genus 4.” Combinatorica, vol. 39, no. 6, Springer
Nature, 2019, pp. 1267–79, doi:10.1007/s00493-019-3905-7.
short: R. Fulek, J. Kynčl, Combinatorica 39 (2019) 1267–1279.
date_created: 2019-11-18T14:29:50Z
date_published: 2019-10-29T00:00:00Z
date_updated: 2025-04-14T13:52:37Z
day: '29'
department:
- _id: UlWa
doi: 10.1007/s00493-019-3905-7
ec_funded: 1
external_id:
arxiv:
- '1709.00508'
isi:
- '000493267200003'
intvolume: ' 39'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1709.00508
month: '10'
oa: 1
oa_version: Preprint
page: 1267-1279
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 261FA626-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02281
name: Eliminating intersections in drawings of graphs
publication: Combinatorica
publication_identifier:
eissn:
- 1439-6912
issn:
- 0209-9683
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Counterexample to an extension of the Hanani-Tutte theorem on the surface of
genus 4
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 39
year: '2019'
...
---
_id: '4069'
abstract:
- lang: eng
text: Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained
by orthogonal projection of the faces of a convex polytope in d + 1 dimensions.
For example, the Delaunay triangulation of a finite point set is such a cell complex.
This paper shows that the in front/behind relation defined for the faces of C
with respect to any fixed viewpoint x is acyclic. This result has applications
to hidden line/surface removal and other problems in computational geometry.
acknowledgement: Research reported in this paper was supported by the National Science
Foundation under grant CCR-8714565.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. Combinatorica.
1990;10(3):251-260. doi:10.1007/BF02122779
apa: Edelsbrunner, H. (1990). An acyclicity theorem for cell complexes in d dimension.
Combinatorica. Springer. https://doi.org/10.1007/BF02122779
chicago: Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.”
Combinatorica. Springer, 1990. https://doi.org/10.1007/BF02122779.
ieee: H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,”
Combinatorica, vol. 10, no. 3. Springer, pp. 251–260, 1990.
ista: Edelsbrunner H. 1990. An acyclicity theorem for cell complexes in d dimension.
Combinatorica. 10(3), 251–260.
mla: Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.”
Combinatorica, vol. 10, no. 3, Springer, 1990, pp. 251–60, doi:10.1007/BF02122779.
short: H. Edelsbrunner, Combinatorica 10 (1990) 251–260.
date_created: 2018-12-11T12:06:45Z
date_published: 1990-09-01T00:00:00Z
date_updated: 2022-02-21T11:08:30Z
day: '01'
doi: 10.1007/BF02122779
extern: '1'
intvolume: ' 10'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02122779
month: '09'
oa_version: None
page: 251 - 260
publication: Combinatorica
publication_identifier:
eissn:
- 1439-6912
issn:
- 0209-9683
publication_status: published
publisher: Springer
publist_id: '2050'
quality_controlled: '1'
scopus_import: '1'
status: public
title: An acyclicity theorem for cell complexes in d dimension
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 10
year: '1990'
...