Project Graph limits and inhomogeneous random graphs

Overview

We have a vivid collaboration with the Extremal graph theory group at the Institute of Computer Science of the Czech Academy of Sciences.

Team members

• Martin Dolezal (January 2018-June 2021)
• Frederik Garbe (April 2018-December 2020)
• Robert Hancock (July-December 2018)
• Jan Hladky (principal investigator, August 2018-June 2021)
• Tomas Juskevicius (October 2020-June 2021)
• Christos Pelekis (January 2018-December 2019)

Papers stemming from the project

Published/accepted

• Ch. Pelekis: On the Shannon entropy of the number of vertices with zero in-degree in randomly oriented hypergraphs
  Le Matematiche 74 (1), 2019, pp. 119-130; [published]; [arXiv]
• K. Engel, Th. Mitsis, Ch. Pelekis, Ch. Reiher: Projection inequalities for antichains
  Israel Journal of Mathematics volume 238, pages 61-90(2020); [published]; [arXiv]
• M. Dolezal, Th. Mitsis, Ch. Pelekis: The de Bruijn-Erdos theorem from a Hausdorff measure point of view
  Acta Mathematica Hungarica 159 (2), 2019, pp. 400-413; [published]; [arXiv]
• Th. Mitsis, Chr. Pelekis, V. Vlasak: A continuous analogue of Erdos' k-Sperner theorem
  Journal of Mathematical Analysis and Applications, Volume 484, Issue 2 (2020), 123754; [published], [arXiv]
• C. Pelekis, V. Vlasak: On k-antichains in the unit n-cube
  Publicationes Mathematica Debrecen, Volume 96, Issue 3-4 (2020), 15; [published]; [arXiv]
• M. Dolezal, J. Hladky, J. Kolar, T. Mitsis, C. Pelekis, V. Vlasak: A Turan-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems
  Discrete & Computational Geometry, 66(1), 281-300 (2021). [arXiv], [published]. [Here] is an identical copy of the published paper available as open access. [Extended abstract] appeared in the proceedings of Eurocomb 2019 [here]
• M. Dolezal, J. Grebik, J. Hladky, I. Rocha, V. Rozhon: Relating the cut distance and the weak* topology for graphons
  Journal of Combinatorial Theory, series B, Volume 147, 2021, Pages 252-298, [arXiv], [published]
• F. Garbe, J. Hladky, J. Lee: Two remarks on graph norms
  Discrete & Computational Geometry, volume 67, pages 919-929 (2022) [arXiv], [published]
• J. Hladky, Ch. Pelekis, M. Sileikis: A limit theorem for small cliques in inhomogeneous random graphs
  Journal of Graph Theory 97 (4), pages 578-599, [arXiv], [published]
• M. Dolezal: Graph limits: An alternative approach to s-graphons
  Journal of Graph Theory 99 (1), page 90-106, [arXiv], [published]
• O. Cooley, F. Garbe, E. K. Hng, M. Kang, N. Sanhueza-Matamala, J. Zalla: Longest paths in random hypergraphs
  SIAM Journal on Discrete Mathematics, 35(4), 2430-2458, [arXiv], [published]
• M. Dolezal, J. Grebik, J. Hladky, I. Rocha, V. Rozhon: Cut distance identifying graphon parameters over weak* limits
  Journal of Combinatorial Theory, series A, volume 189, 105615 [arXiv], [published]
• R. Fokkink, L. Meester, C. Pelekis: Optimizing stakes in simultaneous bets
  ALEA Lat. Am. J. Probab. Math. Stat. 20 (2023), no. 1, 153-165. [arXiv], [published]
• F. Garbe, R. Hancock, J. Hladky, M. Sharifzadeh: Limits of Latin squares
  Discrete Analysis 2023:8, [arXiv], [published]; extended abstract "Theory of limits of sequences of Latin squares" appeared in proceedings of Eurocomb 2019 [here]
• T. Juskevicius: The sharp form of the Kolmogorov-Rogozin inequality and a conjecture of Leader-Radcliffe
  accepted to Bulletin of the London Mathematical Society (2024), [arXiv]

Submitted

• P. Allen, J. Bottcher, D. Clemens, J. Hladky, D. Piguet, A. Taraz: The tree packing conjecture for trees of almost linear maximum degree
  [arXiv]