Gallai-Ramsey numbers involving a rainbow $4$-path

Abstract

Given two non-empty graphs G, H and a positive integer k, the Gallai-Ramsey number gr k (G : H) is defined as the minimum integer N such that for all n ≥ N , every k-edge-coloring of K n contains either a rainbow colored copy of G or a monochromatic copy of H. In this paper, we got some exact values or bounds for gr k (P 5 : H) (k ≥ 3) if H is a general graph or a star with extra independent edges or a pineapple.