Alternating cycles in edge‐colored graphs
Carol Whitehead · Journal of Graph Theory · 1989
Abstract We show that the edges of a 2‐connected graph can be partitioned into two color classes so that every vertex is incident with edges of each color and every alternating cycle passes through a single edge. We also show that the edges of a simple graph with minimum vertex degree δ ≫ 2 can be partitioned into three color classes so that every vertex is incident with edges in exactly two colors and no cycle is alternating.