Gallai-Ramsey number of an 8-cycle. Issue 3 (1st September 2020) - Gregory, Jonathan; Magnant, Colton; Magnant, Zhuojun
Abstract: Given graphs G and H and a positive integer k, the Gallai-Ramsey number g r k ( G : H ) is the minimum integer N such that for any integer n ≥ N, 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 G = 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 = C 8 for all k .