Resumen de New Ramsey multiplicity bounds and search heuristics

Olaf Parczyk, Sebastian Pokutta, Christoph Spiegel, Tibor Szabó

• 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.