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Finite and Descriptive Combinatorics

This is the webpage ( opens in a new window) of the research group "Finite and Descriptive Combinatorics", partially supported the ERC Advanced Grant 101020255 "Finite and Descriptive Combinatorics" (1 January 2022 - 31 December 2026).


In addition to the classical directions of extremal and probabilistic combinatorics (Turan function, Ramsey theory, etc), the group also explores emerging deep connections between combinatorics and other fields such as analysis, descriptive set theory, measured group theory, etc, with applications going both ways. One way of applying analytic techniques to finite graphs will be by means of graph limits (analytic objects of bounded complexity that capture asymptotic properties of large graphs). In the other direction, combinatorial techniques will be applied in search of "constructive'' solutions to some foundational mathematical problems, in particular building upon the recent remarkable results that one can split a 2-dimensional disk into ``definable'' pieces and re-arrange them to form a square.

Group Members

* = co-advised PhD student



All papers (pre-publication versions) should be freely available from Please contact one of the authors if you have difficulty accessing them.

  1. L.Grabowski, A.Mathe, OP: Measurable equidecompositions for group actions with an expansion property, Journal of Eur Math Soc 24 (2022) 4277-4326.
  2. A.Blumenthal, B.Lidicky, Y.Pehova, F.Pfender, OP and J.Volec: Sharp bounds for decomposing graphs into edges and triangles, Combin Prob Comput, 30 (2021) 271-287
  3. H.Liu, OP and K.Staden: The exact minimum number of triangles in graphs of given order and size, Forum of Math, Pi 8 (2020) 144pp.
  4. M.Kang, T.Makai and OP: Supersaturation Problem for the Bowtie, European J Comb 88 (2020) 103107.
  5. JG and OP: Measurable versions of Vizing's theorem, Advances in Mathematics, 374 (2020) paper 107378, 40pp
  6. J.Kim, H.Liu, OP and M.Sharifzadeh: Asymptotic Structure for the Clique Density Theorem, Discrete Analysis (2020) Paper 19, 26pp
  7. OP: Borel Combinatorics of Locally Finite Graphs, in "Surveys in Combinatorics 2021" (edited by K.K.Dabrowski et al), the invited volume of the 28th British Combinatorial Conference, pages 267-319
  8. C.T.Conley, JG and OP: Divisibility of Spheres with Measurable Pieces, accepted by L'Enseignement Mathematique, 34pp.
  9. H.Liu, OP, M.Sharifzadeh and K.Staden: Stability from graph symmetrisation arguments with applications to inducibility, accepted by J London Math Soc, 41 pages
  10. JG and I. Rocha: Fractional Isomorphism of Graphons, Combinatorica, 42 (2022) 365–404
  11. JG: Approximate Schreier decorations and approximate Konig line coloring theorem, Annales Henri Lebesgue, 5 (2022) 303-315.
  12. JG and Z. Vidnyánszky: Tall Fσ subideals of tall analytic ideals, accepted to PAMS, 5pp
  13. JG and OP: Large Deviation Principles for Block and Step Graphon Random Graph Models, 17pp
  14. O.Cooley, M.Kang and OP: On a question of Vera T. Sos about size forcing of graphons, Acta Mathematica Hungarica 168 (2022) 1-26
  15. JG and Vasek Rozhon: Local Problems on Grids from the Perspective of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics (previous, now irrelevant, title: Of Toasts and Tails), 48pp
  16. JG and V.Rozhon: Classification of Local Problems on Paths from the Perspective of Descriptive Combinatorics, extended abstract accepted at EUROCOMB2021, 34pp
  17. OP and K.Staden Stability for the Erdos-Rothschild problem, Forum of Math, Sigma 11 (2023) Paper e23, 43 pages
  18. OP and K.Staden Exact solutions for the Erdos-Rothschild problem, 53pp
  19. S. Brandt, Y. Chang, JG, C. Grunau, V. Rozhoň, Z. Vidnyánszky Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics, 13th Innovations in Theoretical Computer Science Conference, Art. No. 29, 26 pp., LIPIcs. Leibniz Int. Proc. Inform., 215, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2022.
  20. IGF, J.Kim, H.Liu, OP New lower bounds on kissing numbers and spherical codes in high dimensions, 20pp
  21. S. Brandt, Y. Chang, JG, C. Grunau, V. Rozhoň, Z. Vidnyánszky On Homomorphism Graphs, 21pp
  22. V.Falgas-Ravry, OP, E.Vaughan, J.Volec The codegree threshold of K4-, J London Math Soc 107 (2023) 1660-1691
  23. A.Mathe, J.Noel, OP Circle Squaring with Pieces of Small Boundary and Low Borel Complexity, 49 pages
  24. E.Csoka, L.Grabowski, A.Mathe, OP, K.Tyros Moser-Tardos Algorithm with small number of random bits, 31pp.
  25. JG, R. Greenfeld, V. Rozhoň, T. Tao Measurable tilings by abelian group actions, accepted by IMRN, 25pp.
  26. S. Brandt, Y. Chang, JG, C. Grunau, V. Rozhoň, Z. Vidnyánszky Deterministic Distributed algorithms and Descriptive Combinatorics on Δ-regular trees, 47pp.
  27. IGF, JH, H.Liu OP, ZW Disjoint isomorphic balanced clique subdivisions, J Comb Th (B) 161 (2023) 417-436
  28. J. Hou, H. Li, XL, D. Mubayi, Y. Zhang Hypergraphs with infinitely many extremal constructionsLink opens in a new window, Discrete Analysis 2023:18, 34 pp
  29. XL, S. Mukherjee Tight query complexity bounds for learning graph partitionsLink opens in a new window, 35th Annual Conference of Learning Theory (COLT), 2022, 12pp
  30. JH Towards the 0-statement of the Kohayakawa-Kreuter conjecture, Combinatorics, Probability and Computing 23 (2023) 225–268
  31. XL and OP Hypergraph Turan densities can have arbitrarily large algebraic degree, J Comb Th (B) 161 (2023) 407-416
  32. S.Cambie, Y.Dong and MM Extremal values of degree-based entropies of bipartite graphs, 13pp
  33. S.Cambie and MM Resolution of Yan's conjecture on entropy of graphs, accepted by MATCH, 9pp
  34. S.Cambie and MM Extremal entropy for graphs with given size, 8pp.
  35. IGF and H.Liu How to build a pillar: a proof of Thomassen's conjecture, 16pp
  36. IGF, J.Kim, Y.Kim, H.Liu Nested cycles with no geometric crossings, to appear in Proceedings of the American Mathematical Society, 10pp
  37. JG, Z. Vidnyánszky Ramsey, expanders, and Borel chromatic numbers, 11pp
  38. S.Glock, F.Joos, J.Kim, M.Kuhn, L.Lichev and OP On the (6,4)-problem of Brown, Erdos and Sos, 11pp
  39. OP and XL Finite Hypergraph Families with Rich Extremal Turan Constructions via Mixing Patterns, 57pp
  40. ZW Positive co-degree Turan number for C5 and C5- , 8 pages
  41. OP On the limit of the positive l-degree Turan problem, 14pp
  42. J. Hou, H. Li, XL, L.-T. Yuan, and Y. Zhang A step towards a general density Corradi–Hajnal TheoremLink opens in a new window, 32pp
  43. A.Grzesik, D.Kral and OP Forcing Generalized Quasirandom Graphs Efficiently, accepted by Combin Prob Comput, 20pp (Extended abstract)
  44. JG Measurable Vizing's theorem, 25pp.
  45. SS Tilings in quasi-random k-partite hypergraphs, 22pp
  46. C.T.Conley, JG and OP Local version of Vizing's theorem for multi-graphs, 9pp
  47. Y. Chen, XL, J. Nie, and J. Zeng, Random Turan and counting results for general position sets over finite fields, 28pp
  48. XL and J. Song, Exact results for some extremal problems on expansions I,Link opens in a new window 33pp+appendix
  49. XL and J. Song, Hypergraph anti-Ramsey theorems,Link opens in a new window 14pp
  50. J. Hou, C. Hu, H. Li, XL, C. Yang, and Y. Zhang, Toward a density Corradi-Hajnal theorem for degenerate hypergraphs, 37pp
  51. J. Hou, C. Hu, H. Li, XL, C. Yang, and Y. Zhang, Many vertex-disjoint even cycles of fixed length in a graph, 12pp
  52. XL and OP A note on extremal constructions for the Erdos-Rademacher problem, 13pp
  53. JG and OP Large deviation principles for graphon sampling, 42pp.
  54. J. Hou, XL, and H. Zhao Faster coloring and embedding in dense hypergraphs via stabilityLink opens in a new window, 21pp.
  55. C. Helliar and XL A generalized Turan extension of the Deza-Erdos-Frankl Theorem, 12pp.

Talks Given/Forthcoming


  • 11 Oct: OP, Workshop "Measurable, Borel, and Topological Dynamics", CIRM
  • 4 Nov: OP, Workshop "Structure, Sparsity and Randomness", Radbound University, Nijmegen
  • 6 Nov: OP, Old Codger's One-Day Combinatorics Colloquium, Reading
  • 21 Nov: OP, 3in1 Workshop on Graph Theory, Doslonce, Poland
  • 18 Dec: JG, Seminar on Reckoning, Institute of Mathematics of the Czech Academy of Sciences, Prague
  • 20 Dec: JG, Combinatorial group seminar, Institute of Computer Science of the Czech Academy of Sciences, Prague


  • 7 Jan: JG, DIMAP seminar, Warwick University
  • 14 Jan: OP, Warwick Maths Society
  • 30 Jan: OP, ACO Seminar, Carnegie Mellon University
  • 11 Feb: OP, seminar, Adam Mickiewicz University, Poznan
  • 11 Feb: JG, STUK5 mini-talk, Royal Society building, London
  • 17 Feb: OP, Krakow Combinatorics Seminar
  • 11 Mar: JG, Algebra and Geometry Seminar, Lancaster University
  • 20 May: JG, Caltech logic (online) seminar, Caltech
  • 27 Jul: OP, Extremal and Probabilistic Combinatorics Webinar
  • 4 & 7 Aug: JG, Midsummer Combinatorial Workshop XXIV, Charles University, Prague
  • 21 Oct: JG, Probability seminar (online), UBC
  • 10 Nov: OP, UIUC Graph Theory and Combinatorics Seminar
  • 23 Nov: JG, Extremal and Probabilistic Combinatorics Webinar
  • 27 Nov: OP, TU Graz Combinatorics and Optimization Seminar
  • 18 Dec: OP, Combinatorics Seminar of Shandong University


  • 11 Jan: OP, Combinatorics Seminar, Hebrew University of Jerusalem
  • 22 Feb: OP, Caltech Logic Seminar
  • 10 Mar: JG, UBC probability seminar
  • 5 May: IGF, LIMDA Seminar, Universitat Politècnica de Catalunya, Spain
  • 19 May: IGF, Warwick Postgraduate Seminar
  • 1 Jun: JG, Florida Logic seminar
  • 7 Jun: IGF, (Online) Young Researchers in Mathematics Conference, UK
  • 21 Jun: OP, Colloquium Discrete Mathematics and Probability, TU-Graz
  • 23 Jun: OP, Mini-symposium on Extremal and Probabilistic Combinatorics, 8th European Congress of Mathematics
  • 5-9 Jul: OP, the Richard Rado Lecture at the 28th British Combinatorial Conference
  • 26 Jul: IGF, Summer school "Matemáticas: mucho más que números", Universidad de Santiago de Compostela, Spain
  • 6-10 Sep: JG, EUROCOMB 2021, Barcelona
  • 7 Sep: IGF, EUROCOMB 2021, Barcelona
  • 11 Oct: JG, DIMAP seminar, Warwick University
  • 14 Oct: IGF, Discrete Seminar, Umeå University, Sweden
  • 26 Oct: IGF, First Workshop on Developments in Combinatorics, Shandong University, China
  • 8 Nov: JG, Descriptive Dynamics and Combinatorics Seminar, McGill University
  • 12 Nov: IGF, PhD Seminar on Combinatorics, Games and Optimisation, London School of Economics
  • 30 Nov: OP, Warwick Maths Society




  • 29-30 Jan: OP, Workshop on the Foundations of Computation, Sheffield
  • 1 Feb: SS, Combinatorics Seminar, Birmingham
  • 13 Feb: OP, Combinatorial Theory Seminar, Oxford
  • 01 Mar: XL, A Spring Day of Combinatorics, Birmingham

Research visitors

  • 9-12 November 2021: Łukasz Grabowski (Lancaster University)
  • 10-12 May 2022: Péter Pál Pach (Budapest University of Technology and Economics)
  • 16-22 October 2022: Dan Kral' (Masaryk University)
  • 16-22 October 2022: Daniel Ilkovic (Masaryk University)
  • 15-20 January 2023: Jan Volec (Technical University Prague)
  • 4-18 February 2023: Clinton Conley (Carnegie Mellon University)
  • 18-21 February 2023: Mihyun Kang (TU-Graz)