New Lower Bounds for 28 Classical Ramsey Numbers

Geoffrey Exoo, Milos Tatarevic

Abstract


We establish new lower bounds for $28$ classical two and three color Ramsey numbers, and describe the heuristic search procedures used. Several of the new three color bounds are derived from the two color constructions; specifically, we were able to use $(5,k)$-colorings to obtain new $(3,3,k)$-colorings, and $(7,k)$-colorings to obtain new $(3,4,k)$-colorings. Some of the other new constructions in the paper are derived from two well known colorings: the Paley coloring of $K_{101}$ and the cubic coloring of $K_{127}$.


Keywords


Ramsey numbers, edge coloring

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