Papers › The Four-Color Ramsey Multiplicity of Triangles
The Four-Color Ramsey Multiplicity of Triangles
Aldo Kiem, Sebastian Pokutta, Christoph Spiegel
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We study a generalization of a famous result of Goodman and establish that asymptotically at least a 1/256 fraction of all triangles needs to be monochromatic in any four-coloring of the edges of a complete graph. We also show that any large enough extremal construction must be based on a blow-up of one of the two R(3,3,3) Ramsey-colorings of K₁₆. This result is obtained through an efficient flag algebra formulation by exploiting problem-specific combinatorial symmetries that also allows us to study some related problems.
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