Long properly coloured cycles in edge‐coloured graphs

Abstract

Abstract Let be an edge‐coloured graph. The minimum colour degree of is the largest integer such that, for every vertex , there are at least distinct colours on edges incident to . We say that is properly coloured if no two adjacent edges have the same colour. In this paper, we show that, for any and large, every edge‐coloured graph with contains a properly coloured cycle of length at least .