Gallai–Ramsey numbers for cycles

Abstract

For given graphs G and H and an integer k , the Gallai–Ramsey number is defined to be the minimum integer n such that, in any k coloring of the edges of K n , there exists a subgraph isomorphic to either a rainbow coloring of G or a monochromatic coloring of H . In this work, we consider Gallai–Ramsey numbers for the case when G = K 3 and H is a cycle of a fixed length.