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Anti-Ramsey numbers for disjoint copies of graphs

Gorgol I., Gorlich A.

Opuscula Mathematica

2017

Vol. 37, no. 4

567--575

A subgraph of an edge-colored graph is called rainbow if all of its edges have different colors. For a graph G and a positive integer n, the anti-Ramsey number ar(n,G) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of H. Anti-Ramsey numbers were introduced by Erdos, Simonovits and Sós and studied in numerous papers. Let G be a graph with anti-Ramsey number ar(n, G). In this paper we show the lower bound for ar(n,pG), where pG denotes p vertex-disjoint copies of G. Moreover, we prove that in some special cases this bound is sharp.