Rainbow disjoint union of P4 and a matching in complete graphs

Abstract

An edge-colored graph G is called rainbow if all the colors on its edges are distinct. Given graphs G and H, the anti-Ramsey number AR(G,H) is the maximum number k such that there exists an edge-coloring of G with exactly k colors containing no rainbow copy of H. Recently, the anti-Ramsey problem for disjoint union of graphs received much attention. In particular, several researchers focused on the problem for graphs consisting of small components. In this paper, we continue the work in this line. We refine the bound of n and determine the precise value of AR(Kn,P4∪tP2) for all n≥2t+4 in complete graphs.