Anti-Ramsey problems in the generalized Petersen graphs for cycles

Abstract

The anti-Ramsey number Ar(G, H) is the maximum number of colors in an edge-coloring of G with no rainbow copy of H. In this paper, we determine the exact anti-Ramsey number in the generalized Petersen graph P n,k for cycles C d , where 1 ≤ k ≤ n−1 2 and 5 ≤ d ≤ 6. We also give an algorithm to obtain the upper bound or lower bound of anti-Ramsey number.