Gallai-Ramsey number of an 8-cycle

Abstract

Given graphs G and H and a positive integer k, the Gallai-Ramsey number gr k ðG : HÞ is the minimum integer N such that for any integer n ! N, every k-edge-coloring of K n contains either a rainbow copy of G or a monochromatic copy of H. These numbers have recently been studied for the case when G ¼ K 3 , 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 H ¼ C 8 for all k.