Rainbow disjoint union of clique and matching in edge-colored complete graph
Zemin Jin, Junqi Gu · Discussiones Mathematicae Graph Theory · 2023
Given an edge-coloring of a graph G, G is said to be rainbow if any two edges of G receive different colors.The anti-Ramsey number AR(G, H) is defined to be the maximum integer k such that there exists a k-edgecoloring of G avoiding rainbow copies of H.The anti-Ramsey number for graphs, especially matchings, have been studied in several graph classes.Gilboa and Roditty focused on the anti-Ramsey number of graphs with small components, especially including a matching.In this paper, we continue the work in this direct and determine the exact value of the anti-Ramsey number of K 4 ∪ tP 2 in complete graphs.Also, we improve the bound and obtain the exact value of AR(K n , C 3 ∪ tP 2 ) for all n ≥ 2t + 3.