# New Ramsey Multiplicity Bounds and Search Heuristics

@inproceedings{Parczyk2022NewRM, title={New Ramsey Multiplicity Bounds and Search Heuristics}, author={Olaf Parczyk and Sebastian Pokutta and Christoph Spiegel and T'i mea Szab'o}, year={2022} }

We study two related problems concerning the number of monochromatic cliques in twocolorings of the complete graph that go back to questions of Erdős. Most notably, we improve the 25-year-old upper bounds of Thomason on the Ramsey multiplicity of K4 and K5 and we settle the minimum number of independent sets of size 4 in graphs with clique number at most 4. Motivated by the elusiveness of the symmetric Ramsey multiplicity problem, we also introduce an off-diagonal variant and obtain tight…

## One Citation

Ramsey multiplicity and the Tur\'an coloring

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Extending an earlier conjecture of Erd˝os, Burr and Rosta conjectured that among all two-colorings of the edges of a complete graph, the uniformly random coloring asymptotically minimizes the number…

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