New Ramsey multiplicity bounds and search heuristics

• Olaf Parczyk ^[1] ; Sebastian Pokutta ; Christoph Spiegel ; Tibor Szabó ^[1]
  1. [1] Freie Universität Berlin
• Localización: Discrete Mathematics Days 2022 / coord. por Luis Felipe Tabera Alonso, 2022, ISBN 978-84-19024-02-2, págs. 224-230
• Idioma: inglés
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• Resumen

  • We study two related problems concerning the number of monochromatic cliques intwo-colorings of the complete graph that go back to questions of Erd˝os. Most notably,we improve the 25-year-old upper bound of the K4 and K5 Ramsey multiplicity due toThomason and settle the minimum number of independent sets of size 4 in graphs withclique number at most 4. We also introduce a notion of off-diagonal Ramsey multiplicity,obtaining two tight results when counting triangles in one color, and more broadly motivatethis question by relating it to the study of which pairs of clique and independent set densitiescan be realized as the limit of some sequence of graphs.