Finite and Descriptive Combinatorics

Project Information

FDC

Grant agreement ID: 101020255

DOI

10.3030/101020255

EC signature date 27 May 2021

Start date 1 January 2022

End date 31 December 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 581 387,00

EU contribution

€ 1 581 387,00

Coordinated by

UNIVERSITY OF WARWICK
United Kingdom

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Other (30)

New bounds for the optimal density of covering single-insertion codes via the Turán density

Author(s): Oleg Pikhurko, Oleg Verbitsky, Maksim Zhukovskii
Published in: 2024
Publisher: Cornell University

Random Turán and counting results for general position sets over finite fields

Author(s): Yaobin Chen, Xizhi Liu, Jiaxi Nie, Ji Zeng
Published in: 2023
Publisher: arxiv

Fractional Divisibility of Spheres with Partially Generic Sets of Rotations

Author(s): Jan Grebík, Christian Ikenmeyer, O.Pikhurko
Published in: 2025
Publisher: arxiv.org

Positive codegree Andrásfai--Erdős--Sós theorem for the generalized triangle

Author(s): Xizhi Liu, Sijie Ren, Jian Wang
Published in: 2024
Publisher: Cornell University

Exact results for some extremal problems on expansions I

Author(s): Xizhi Liu, Jialei Song
Published in: 2023
Publisher: arxiv

Tight bounds for rainbow partial F-tiling in edge-colored complete hypergraphs

Author(s): Jinghua Deng, Jianfeng Hou, Xizhi Liu, Caihong Yang
Published in: 2024
Publisher: arxiv.org

Large deviation principles for graphon sampling

Author(s): Grebík, Jan; Pikhurko, Oleg
Published in: Issue 15, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2311.06531

On the boundedness of degenerate hypergraphs

Author(s): Jianfeng Hou, Caiyun Hu, Heng Li, Xizhi Liu, Caihong Yang, Yixiao Zhang
Published in: 2024
Publisher: arxiv.org

Density Hajnal--Szemerédi theorem for cliques of size four

Author(s): Jianfeng Hou, Caiyun Hu, Xizhi Liu, Yixiao Zhang
Published in: 2025
Publisher: Cornell University

Uniquely colorable hypergraphs

Author(s): Xizhi Liu, Jie Ma, Tianhen Wang, Tianming Zhu
Published in: 2024
Publisher: Cornell University

A step towards a general density Corr\'{a}di--Hajnal Theorem

Author(s): Hou, Jianfeng; Li, Heng; Liu, Xizhi; Yuan, Long-Tu; Zhang, Yixiao
Published in: 2023
Publisher: arxiv.org
DOI: 10.48550/arxiv.2302.09849

Nondegenerate Turán problems under (t,p)-norms

Author(s): Wanfang Chen, Daniel Iľkovič, Jared León, Xizhi Liu, Oleg Pikhurko
Published in: 2024
Publisher: arxiv.org

Many vertex-disjoint even cycles of fixed length in a graph

Author(s): Jianfeng Hou, Caiyun Hu, Heng Li, Xizhi Liu, Caihong Yang, Yixiao Zhang
Published in: 2023
Publisher: arxiv

Finite Hypergraph Families with Rich Extremal Turán Constructions via Mixing Patterns

Author(s): Liu, Xizhi; Pikhurko, Oleg
Published in: 2022
Publisher: arxiv.org
DOI: 10.48550/arxiv.2212.08636

New lower bounds on kissing numbers and spherical codes in high dimensions

Author(s): Irene Gil Fernández, Jaehoon Kim, Hong Liu, Oleg Pikhurko
Published in: 2023
Publisher: Cornell University

A note on the minimum size of Turán systems

Author(s): Xizhi Liu, Oleg Pikhurko
Published in: 2025
Publisher: arxiv.org

On a hypergraph Mantel theorem

Author(s): Xizhi Liu
Published in: 2025
Publisher: arxiv.org

The Turán density of the tight 5-cycle minus one edge

Author(s): Levente Bodnár, Jared León, Xizhi Liu, Oleg Pikhurko
Published in: 2024
Publisher: Cornell University

Phase transition of degenerate Turán problems in p-norms

Author(s): Jun Gao, Xizhi Liu, Jie Ma, Oleg Pikhurko
Published in: 2024
Publisher: Cornell University

Tilings in quasi-random k-partite hypergraphs

Author(s): Sun, Shumin
Published in: 2023
Publisher: arxiv.org
DOI: 10.48550/arxiv.2306.10539

Generalized Andrásfai--Erdős--Sós theorems for odd cycles

Author(s): Zian Chen, Jianfeng Hou, Caiyun Hu, Xizhi Liu
Published in: 2024
Publisher: Cornell University

A criterion for Andrásfai--Erdős--Sós type theorems and applications

Author(s): Jianfeng Hou, Xizhi Liu, Hongbin Zhao
Published in: 2024
Publisher: arxiv

Strong stability from vertex-extendability and applications in generalized Turán problems

Author(s): Wanfang Chen, Xizhi Liu
Published in: 2024
Publisher: arxiv

Circle Squaring with Pieces of Small Boundary and Low Borel Complexity

Author(s): Máthé, András; Noel, Jonathan A.; Pikhurko, Oleg
Published in: Issue 1, 2022
Publisher: arxiv.org

On the (k+2,k)-problem of Brown, Erdos and Sos for k=5,6,7

Author(s): Stefan Glock, Jaehoon Kim, Lyuben Lichev, Oleg Pikhurko, Shumin Sun
Published in: 2024
Publisher: arxiv.org

Moser-Tardos Algorithm with small number of random bits

Author(s): Endre Csóka, Łukasz Grabowski, András Máthé, Oleg Pikhurko, Konstantinos Tyros
Published in: 2022
Publisher: arxiv.org
DOI: 10.48550/arxiv.2203.05888

Toward a density Corrádi--Hajnal theorem for degenerate hypergraphs

Author(s): Jianfeng Hou, Caiyun Hu, Heng Li, Xizhi Liu, Caihong Yang, Yixiao Zhang
Published in: 2023
Publisher: arxiv

Andrásfai--Erdős--Sós theorem for the generalized triangle

Author(s): Xizhi Liu, Sijie Ren, Jian Wang
Published in: 2024
Publisher: Cornell University

Tiling H in dense graphs

Author(s): Nannan Chen, Xizhi Liu, Lin Sun, Guanghui Wang
Published in: 2025
Publisher: arxiv.org

A generalized Turán extension of the Deza--Erdős--Frankl Theorem

Author(s): Charlotte Helliar, Xizhi Liu
Published in: 2024
Publisher: arxiv

Peer reviewed articles (20)

On a question of Vera T. Sos about size forcing of graphons

Author(s): Cooley, Oliver; Kang, Mihyun; Pikhurko, Oleg
Published in: Acta Mathematica Hungarica, Issue 168, 2022, Page(s) 1-26, ISSN 0236-5294
Publisher: Springer Netherlands
DOI: 10.1007/s10474-022-01265-8

Stability for the Erdős-Rothschild problem

Author(s): Pikhurko, Oleg; Staden, Katherine
Published in: Forum of Mathematics Sigma, Issue 11, 2023, Page(s) 43pp, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2023.12

Forcing Generalized Quasirandom Graphs Efficiently

Author(s): Grzesik, Andrzej; Kral, Daniel; Pikhurko, Oleg
Published in: Combinatorics, Probability and Computing, Issue 33, 2024, Page(s) 16-31, ISSN 0963-5483
Publisher: Cambridge University Press
DOI: 10.1017/s0963548323000263

Hypergraphs with infinitely many extremal constructions

Author(s): Hou, Jianfeng; Li, Heng; Liu, Xizhi; Mubayi, Dhruv; Zhang, Yixiao
Published in: Dicrete Analysis, Issue 18, 2023, Page(s) 34pp, ISSN 2397-3129
Publisher: arxiv.org
DOI: 10.48550/arxiv.2206.03948

The codegree threshold of K_4-

Author(s): Falgas‐Ravry, Victor; Pikhurko, Oleg; Vaughan, Emil; Volec, Jan
Published in: Journal of the London Mathematical Society, Issue 107, 2023, Page(s) 1660–1691, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12722

A note on extremal constructions for the Erdős–Rademacher problem

Author(s): Xizhi Liu, Oleg Pikhurko
Published in: Combinatorics, Probability and Computing, Issue 34, 2024, Page(s) 52-62, ISSN 0963-5483
Publisher: Cambridge University Press
DOI: 10.1017/s0963548324000269

Exact solutions to the Erdős-Rothschild problem

Author(s): Oleg Pikhurko, Katherine Staden
Published in: Forum of Mathematics, Sigma, Issue 12, 2024, Page(s) 1-45, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2023.117

Local version of Vizing's theorem for multigraphs

Author(s): Clinton T. Conley, Jan Grebík, Oleg Pikhurko
Published in: Journal of Graph Theory, Issue 107, 2024, Page(s) 693-701, ISSN 0364-9024
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/jgt.23155

Stability from graph symmetrisation arguments with applications to inducibility

Author(s): Hong Liu, Oleg Pikhurko, Maryam Sharifzadeh, Katherine Staden
Published in: Journal of the London Mathematical Society, Issue 108, 2023, Page(s) 1121-1162, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12777

On the limit of the positive $\ell$-degree Tur\'an problem

Author(s): Pikhurko, Oleg
Published in: Electronic Journal of Combinatorics, Issue 30, 2023, Page(s) Paper 3.25, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/11912

New Lower Bound on Ball Packing Density in High-Dimensional Hyperbolic Spaces

Author(s): Irene Gil Fernández, Jaehoon Kim, Hong Liu, Oleg Pikhurko
Published in: International Mathematics Research Notices, Issue 2025, 2025, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnae282

Measurable equidecompositions for group actions with an expansion property

Author(s): Grabowski, Lukasz; Máthé, András; Pikhurko, Oleg
Published in: Journal of the European Mathematical Society, Issue 24, 2022, Page(s) 4277-4326, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1189

Hypergraph Anti‐Ramsey Theorems

Author(s): Xizhi Liu, Jialei Song
Published in: Journal of Graph Theory, 2024, ISSN 0364-9024
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/jgt.23204

Turán problems in pseudorandom graphs

Author(s): Xizhi Liu, Dhruv Mubayi, David Munhá Correia
Published in: Combinatorics, Probability and Computing, Issue 33, 2024, Page(s) 583-596, ISSN 0963-5483
Publisher: Cambridge University Press
DOI: 10.1017/s0963548324000142

Towards the 0-statement of the Kohayakawa-Kreuter conjecture

Author(s): Hyde, Joseph
Published in: Combinatorics, Probability and Computing, Issue 32, 2023, Page(s) 225-268, ISSN 0963-5483
Publisher: Cambridge University Press
DOI: 10.1017/s0963548322000219

Divisibility of spheres with measurable pieces

Author(s): Clinton T. Conley, Jan Grebik, Oleg Pikhurko
Published in: L’Enseignement Mathématique, Issue 70, 2024, Page(s) 25-59, ISSN 0013-8584
Publisher: Fondation L’Enseignement Mathématique
DOI: 10.4171/lem/1058

Hypergraph Turán densities can have arbitrarily large algebraic degree

Author(s): Liu, Xixhi; Pikhurko, Oleg
Published in: Journal of Combinatorial Theory, Series B, Issue 161, 2023, Page(s) 407-416, ISSN 0095-8956
Publisher: Academic Press
DOI: 10.1016/j.jctb.2023.03.003

Constructions of Turán systems that are tight up to a multiplicative constant

Author(s): Oleg Pikhurko
Published in: Advances in Mathematics, Issue 464, 2025, Page(s) 110148, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2025.110148

On the $(6,4)$-problem of Brown, Erdős and Sós

Author(s): Glock, Stefan; Joos, Felix; Kim, Jaehoon; Kühn, Marcus; Lichev, Lyuben; Pikhurko, Oleg
Published in: Proceedings of the Ame, Issue 11, 2024, Page(s) 173-186, ISSN 2330-1511
Publisher: AMS
DOI: 10.1090/bproc/170

Disjoint isomorphic balanced clique subdivisions

Author(s): Gil Fernandez, Irene; Hyde, Joseph; Liu, Hong, Pikhurko, Oleg; Wu, Zhuo
Published in: Journal of Combinatorial Theory, Series B, Issue 161, 2023, Page(s) 417-436, ISSN 0095-8956
Publisher: Academic Press
DOI: 10.1016/j.jctb.2023.03.002