Gallai-Ramsey number of an 8-cycle

Abstract

Given graphs G and H and a positive integer k, the Gallai-Ramsey number is the minimum integer N such that for any integer every k-edge-coloring of Kn contains either a rainbow copy of G or a monochromatic copy of H. These numbers have recently been studied for the case when where still only a few precise numbers are known for all k. In this paper, we extend the known precise Gallai-Ramsey numbers to include for all k.