Finite and Descriptive Combinatorics

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Publications

Finite Hypergraph Families with Rich Extremal Turán Constructions via Mixing Patterns

Author(s): Xizhi Liu, Oleg Pikhurko
Published in: Forum of Mathematics, Sigma, Issue 13, 2025, ISSN 2050-5094
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/fms.2025.12

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: IEEE Transactions on Information Theory, Issue 71, 2025, Page(s) 4260-4266, ISSN 0018-9448
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tit.2025.3557393

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: Journal of Combinatorial Theory, Series B, Issue 172, 2025, Page(s) 221-262, ISSN 0095-8956
Publisher: Academic Press
DOI: 10.1016/j.jctb.2025.01.001

Positive Codegree Andrásfai–Erdős–Sós Theorem for the Generalized Triangle

Author(s): Xizhi Liu, Sijie Ren, Jian Wang
Published in: Journal of Graph Theory, Issue 112, 2026, Page(s) 54-61, ISSN 0364-9024
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/jgt.70012

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

Tight Bounds for Rainbow Partial F‐Tiling in Edge‐Colored Complete Hypergraphs

Author(s): Jinghua Deng, Jianfeng Hou, Xizhi Liu, Caihong Yang
Published in: Journal of Graph Theory, Issue 110, 2025, Page(s) 457-467, ISSN 0364-9024
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/jgt.23282

On the Boundedness of Degenerate Hypergraphs

Author(s): Jianfeng Hou, Caiyun Hu, Heng Li, Xizhi Liu, Caihong Yang, Yixiao Zhang
Published in: Acta Mathematica Sinica, English Series, Issue 42, 2026, Page(s) 464-480, ISSN 1439-8516
Publisher: Springer Verlag
DOI: 10.1007/s10114-026-4419-z

A step towards a general density Corrádi–Hajnal theorem

Author(s): Jianfeng Hou, Heng Li, Xizhi Liu, Long-Tu Yuan, Yixiao Zhang
Published in: Canadian Journal of Mathematics, 2025, Page(s) 1-36, ISSN 0008-414X
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008414x25000197

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

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: American Journal of Mathematics, Issue 147, 2025, Page(s) 901-925, ISSN 1080-6377
Publisher: Project MUSE
DOI: 10.1353/ajm.2025.a966288

Semi-inducibility of 4-vertex graphs

Author(s): Levente Bodnár, Oleg Pikhurko
Published in: Discrete Applied Mathematics, Issue 392, 2026, Page(s) 303-323, ISSN 0166-218X
Publisher: Elsevier BV
DOI: 10.1016/j.dam.2026.06.003

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

Phase Transition of Degenerate Turán Problems in ${p}$-Norms

Author(s): Jun Gao, Xizhi Liu, Jie Ma, Oleg Pikhurko
Published in: SIAM Journal on Discrete Mathematics, Issue 39, 2025, Page(s) 1712-1736, ISSN 0895-4801
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/25m1738401

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

A Note on the Minimum Size of Turán Systems

Author(s): Xizhi Liu, Oleg Pikhurko
Published in: The Electronic Journal of Combinatorics, Issue 33, 2026, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/14584

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

Circle squaring with pieces of small boundary and low Borel complexity

Author(s): András Máthé, Jonathan A. Noel, Oleg Pikhurko
Published in: Advances in Mathematics, Issue 484, 2025, Page(s) 110685, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2025.110685

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

On the ($k + \text{2}, k$)-problem of Brown, Erdős, and Sós for $k =$ 5,6,7

Author(s): Stefan Glock, Jaehoon Kim, Lyuben Lichev, Oleg Pikhurko, Shumin Sun
Published in: Canadian Journal of Mathematics, 2025, Page(s) 1-43, ISSN 0008-414X
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008414x25000021

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

Convergence of spectra of digraph limits

Author(s): Jan Grebík, Daniel Král’, Xizhi Liu, Oleg Pikhurko, Julia Slipantschuk
Published in: European Journal of Combinatorics, Issue 134, 2026, Page(s) 104349, ISSN 0195-6698
Publisher: Academic Press
DOI: 10.1016/j.ejc.2026.104349

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

Author(s): Yaobin Chen, Xizhi Liu, Jiaxi Nie, Ji Zeng
Published in: Science China Mathematics, Issue 68, 2025, Page(s) 3043-3062, ISSN 1674-7283
Publisher: Zhongguo Kexue Zazhishe/Science in China Press
DOI: 10.1007/s11425-024-2384-x

A Criterion for Andrásfai–Erdős–Sos Type Theorems and Applications

Author(s): Jianfeng Hou, Xizhi Liu, Hongbin Zhao
Published in: Annals of Applied Mathematics, Issue 41, 2026, Page(s) 377-404, ISSN 3105-2266
Publisher: Global Science Press
DOI: 10.4208/aam.oa-2025-0015

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

Set families: restricted distances via restricted intersections

Author(s): ZICHAO DONG, JUN GAO, HONG LIU, MINGHUI OUYANG, QIANG ZHOU
Published in: Mathematical Proceedings of the Cambridge Philosophical Society, 2026, Page(s) 1-20, ISSN 0305-0041
Publisher: Cambridge University Press
DOI: 10.1017/s0305004126101984

Sabotaging Mantel's Theorem

Author(s): Natalie Behague, Debsoumya Chakraborti, Xizhi Liu
Published in: The Electronic Journal of Combinatorics, Issue 33, 2026, ISSN 1077-8926
Publisher: Electronic Journal of Combinatorics
DOI: 10.37236/14324

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

Exact Results for Some Extremal Problems on Expansions I

Author(s): Xizhi Liu, Jialei Song, Long-Tu Yuan
Published in: Communications in Mathematics and Statistics, 2025, ISSN 2194-6701
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40304-024-00429-y

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

New upper bound for lattice covering by spheres

Author(s): Jun Gao, Xizhi Liu, Oleg Pikhurko, Shumin Sun
Published in: Mathematika, Issue 72, 2026, ISSN 0025-5793
Publisher: University College London, Department of Mathematics
DOI: 10.1112/mtk.70066

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

A Generalized Turán Extension of the Deza–Erdős–Frankl Theorem

Author(s): Charlotte Helliar, Xizhi Liu
Published in: Journal of Graph Theory, Issue 112, 2026, Page(s) 161-171, ISSN 0364-9024
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/jgt.70023

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: Journal of Graph Theory, Issue 111, 2026, Page(s) 67-77, ISSN 0364-9024
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/jgt.70003

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

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

Exact results for some extremal problems on expansions I

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

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

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

Rational codegree Turán density of hypergraphs

Author(s): Jun Gao, Oleg Pikhurko, Mingyuan Rong, Shumin Sun
Published in: 2026
Publisher: arixv.org

Uniquely colorable hypergraphs

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

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

Intervals of uniform Turán densities

Author(s): Heng Li, Xizhi Liu, Oleg Pikhurko
Published in: 2026
Publisher: arxiv

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

On cliques in hypergraphs

Author(s): Jun Gao
Published in: 2025
Publisher: arxiv.org

Intervals of hypergraph Turán densities

Author(s): Xizhi Liu, Oleg Pikhurko
Published in: 2026
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

A note on the minimum size of Turán systems

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

Covering large-dimensional Euclidean spaces by random translates of a given convex body

Author(s): Boris Bukh, Jun Gao, Xizhi Liu, Oleg Pikhurko, Shumin Sun
Published in: 2025
Publisher: arxiv

On a hypergraph Mantel theorem

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

Turán density of tight cycles minus one edge in the ℓ2 -norm

Author(s): Levente Bodnár, Jinghua Deng, Jianfeng Hou, Xizhi Liu, Hongbin Zhao
Published in: 2025
Publisher: arxiv

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

Strong non-principality of positive codegree Turán density

Author(s): Levente Bodnár, Jun Gao, Oleg Pikhurko, Mingyuan Rong, Shumin Sun
Published in: 2026
Publisher: arxiv.org

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

The inducibility of 6-vertex graphs

Author(s): Levente Bodnár, Jun Gao, Jared León, Xizhi Liu
Published in: 2026
Publisher: arxiv

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

Chromatic thresholds for pairs of graphs

Author(s): Jun Gao, Hong Liu, Zhuo Wu, Yisai Xue
Published in: 2026
Publisher: arxiv.org

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

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

The Turán density of short tight cycles

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

Tiling H in dense graphs

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

Induced rational exponents and bipartite subgraphs in Ks,s-free graphs

Author(s): Zichao Dong, Jun Gao, Ruonan Li, Hong Liu
Published in: 2025
Publisher: arxiv.org

A note on the Ratio and Inertia Bounds for the k-Independence Number

Author(s): Jun Gao, Jie Ma, Oleg Pikhurko
Published in: 2026
Publisher: arxiv.org

Tight query complexity bounds for learning graph partitions

Author(s): Xizhi Liu, Sayan Mukherjee
Published in: Proceedings of Thirty Fifth Conference on Learning Theory, PMLR, Issue 178, 2022, Page(s) 167-181
Publisher: ML Research Press

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