Anti-Ramsey numbers for cycles in n-prisms

Abstract

An edge colored graph is called rainbow if all the colors on its edges are distinct. A rainbow copy of a graph H in an edge colored graph G is a subgraph of G isomorphic to H such that the coloring restricted to H is rainbow. Let G and H be two graphs. The anti-Ramsey number A r ( G , H ) is the maximum number of colors in an edge coloring of G which has no rainbow copy of H . For n ≥ 3 , the n -prism is the cartesian product C n □ K 2 . In this paper, we determine the anti-Ramsey numbers for cycles in n -prisms.