A characterization of cut-percolating bigraphs

Primarily AI-generated textHuman understanding: some partsmath.CO — Combinatoricsmath.GR — Group Theorycs.DM — Discrete Mathematics

Contributed by Václav Rozhoň ↗

Version 1 / Oct 11, 2026 / CC BY 4.0

Abstract

Conlon and Lee introduced reflection bigraphs and cut-percolation in their study of graph norms. We prove that, for connected bigraphs, these two notions coincide, confirming their prediction.

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References

  1. C. Amarra, A. Devillers, and C. E. Praeger, Chain-imprimitive, flag-transitive 22-designs , Designs, Codes and Cryptography 92 (2024), 2491--2510. doi:10.1007/s10623-024-01400-2 (https://doi.org/10.1007/s10623-024-01400-2). arXiv:2401.13885 (https://arxiv.org/abs/2401.13885).arXivDOI
  2. L. Babai, Graph isomorphism in quasipolynomial time , Proceedings of the 48th Annual ACM Symposium on Theory of Computing (STOC 2016), 684--697. Corrected full version 2.5 (2018) (https://people.cs.uchicago.edu/~laci/quasi25.pdf).link
  3. A. K. Barnhill, The FAn\mathrm{FA}_n conjecture for Coxeter groups , Algebraic & Geometric Topology 6 (2006), 2117--2150. doi:10.2140/agt.2006.6.2117 (https://doi.org/10.2140/agt.2006.6.2117).DOI
  4. J. Baek, D. Conlon, and J. Lee, On the extremal number of incidence graphs , to appear in Journal of Combinatorial Theory, Series B. Preprint: arXiv:2501.00521v1 (https://arxiv.org/abs/2501.00521v1), 2024.arXiv
  5. S. Basu, R. Pollack, and M.-F. Roy, Algorithms in Real Algebraic Geometry , 2nd ed., Algorithms and Computation in Mathematics 10, Springer, 2006. doi:10.1007/3-540-33099-2 (https://doi.org/10.1007/3-540-33099-2).DOI
  6. N. Brady, J. P. McCammond, B. Mühlherr, and W. D. Neumann, Rigidity of Coxeter groups and Artin groups , Geometriae Dedicata 94 (2002), 91--109. Author manuscript (https://web.math.ucsb.edu/~mccammon/papers/rigidity.pdf).link
  7. F. R. K. Chung, R. L. Graham, and R. M. Wilson, Quasi-random graphs , Combinatorica 9 (1989), 345--362. Full text (https://mathweb.ucsd.edu/~ronspubs/89_05_quasi_graphs.pdf).link
  8. D. Conlon, J. Fox, and B. Sudakov, An approximate version of Sidorenko's conjecture , Geometric and Functional Analysis 20 (2010), 1354--1366. doi:10.1007/s00039-010-0097-0 (https://doi.org/10.1007/s00039-010-0097-0). arXiv:1004.4236 (https://arxiv.org/abs/1004.4236).arXivDOI
  9. D. Conlon, J. H. Kim, C. Lee, and J. Lee, Some advances on Sidorenko's conjecture , Journal of the London Mathematical Society 98 (2018), 593--608. doi:10.1112/jlms.12142 (https://doi.org/10.1112/jlms.12142). arXiv:1510.06533 (https://arxiv.org/abs/1510.06533).arXivDOI
  10. D. Conlon and J. Lee, Finite reflection groups and graph norms , Advances in Mathematics 315 (2017), 130--165. doi:10.1016/j.aim.2017.05.009 (https://doi.org/10.1016/j.aim.2017.05.009). Preprint version used for numbering: arXiv:1611.05784v2 (https://arxiv.org/abs/1611.05784v2).arXivDOI
Show all 29 referencesShow fewer references
  1. D. Conlon and J. Lee, Domination inequalities and dominating graphs , Math. Proc. Cambridge Philos. Soc. 177 (2024), 167--184. doi:10.1017/S0305004124000185 (https://doi.org/10.1017/S0305004124000185). arXiv:2303.01997v2 (https://arxiv.org/abs/2303.01997v2).arXivDOI
  2. L. N. Coregliano, Bigraph percolation problems , arXiv:2408.14257v2 (https://arxiv.org/abs/2408.14257v2), 2024.arXiv
  3. L. N. Coregliano, Left-cut-percolation and induced-Sidorenko bigraphs , SIAM J. Discrete Math. 38 (2024), 1586--1629. doi:10.1137/22M1526794 (https://doi.org/10.1137/22M1526794). arXiv:2205.14703 (https://arxiv.org/abs/2205.14703).arXivDOI
  4. M. Doležal, J. Grebík, J. Hladký, I. Rocha, and V. Rozhoň, Cut distance identifying graphon parameters over weak* limits , Journal of Combinatorial Theory, Series A 189 (2022), 105615. doi:10.1016/j.jcta.2022.105615 (https://doi.org/10.1016/j.jcta.2022.105615). Preprint: arXiv:1809.03797v5 (https://arxiv.org/abs/1809.03797v5).arXivDOI
  5. D. Eppstein, Reset sequences for monotonic automata , SIAM Journal on Computing 19 (1990), 500--510. doi:10.1137/0219033 (https://doi.org/10.1137/0219033).DOI
  6. M. Fiedler, Algebraic connectivity of graphs , Czechoslovak Mathematical Journal 23 (1973), 298--305. Full text (https://dml.cz/handle/10338.dmlcz/101168).link
  7. F. Garbe, J. Hladký, and J. Lee, Two remarks on graph norms , Discrete & Computational Geometry 67 (2022), 919--929. doi:10.1007/s00454-021-00280-w (https://doi.org/10.1007/s00454-021-00280-w).DOI
  8. P. Potočnik, with S. Wilson and other collaborators, Datasets of Highly Symmetric Objects . The locally arc-transitive valence-{3,4}\{3,4\} and semisymmetric valence-four catalogues, accessed October 2026. https://graphsym.net/.link
  9. H. Hatami, Graph norms and Sidorenko's conjecture , Israel Journal of Mathematics 175 (2010), 125--150. arXiv:0806.0047 (https://arxiv.org/abs/0806.0047).arXiv
  10. J. E. Humphreys, Reflection Groups and Coxeter Groups , Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, 1990.
  11. D. Král', T. Martins, P. P. Pach, and M. Wrochna, The step Sidorenko property and non-norming edge-transitive graphs , Journal of Combinatorial Theory, Series A 162 (2019), 34--54. Preprint: arXiv:1802.05007v4 (https://arxiv.org/abs/1802.05007v4).arXiv
  12. J. Lee and B. Schülke, Convex graphon parameters and graph norms , Israel Journal of Mathematics 242 (2021), 549--563. doi:10.1007/s11856-021-2112-6 (https://doi.org/10.1007/s11856-021-2112-6). Preprint: arXiv:1910.08454v2 (https://arxiv.org/abs/1910.08454v2).arXivDOI
  13. L. Lovász, Large Networks and Graph Limits , American Mathematical Society Colloquium Publications 60, American Mathematical Society, Providence, RI, 2012. doi:10.1090/coll/060 (https://doi.org/10.1090/coll/060).DOI
  14. E. M. Luks, Isomorphism of graphs of bounded valence can be tested in polynomial time , Journal of Computer and System Sciences 25 (1982), 42--65. doi:10.1016/0022-0000(82)90009-5 (https://doi.org/10.1016/0022-0000(82)90009-5).DOI
  15. P. Potočnik and S. E. Wilson, Recipes for edge-transitive tetravalent graphs , Art of Discrete and Applied Mathematics 3 (2020), #P1.08. doi:10.26493/2590-9770.1269.732 (https://doi.org/10.26493/2590-9770.1269.732). arXiv:1608.04158 (https://arxiv.org/abs/1608.04158).arXivDOI
  16. Á. Seress, Permutation Group Algorithms , Cambridge Tracts in Mathematics 152, Cambridge University Press, 2003.
  17. A. Sidorenko, A correlation inequality for bipartite graphs , Graphs and Combinatorics 9 (1993), 201--204. doi:10.1007/BF02988307 (https://doi.org/10.1007/BF02988307).DOI
  18. A. Sidorenko, Weakly norming graphs are edge-transitive , Combinatorica 40 (2020), 601--604. doi:10.1007/s00493-020-4468-3 (https://doi.org/10.1007/s00493-020-4468-3). arXiv:2003.13598 (https://arxiv.org/abs/2003.13598).arXivDOI
  19. A. Thomason, Pseudo-random graphs , in Random Graphs '85, North-Holland Mathematics Studies 144, North-Holland, Amsterdam, 1987, 307--331. doi:10.1016/S0304-0208(08)73063-9 (https://doi.org/10.1016/S0304-0208(08)73063-9).DOI

Version history

  1. v1Submitted by Václav RozhoňInitial depositCurrentOct 11, 2026