M2-Edge Colorings Of Cacti And Graph Joins - Czap Július; Šugerek Peter; Ivančo Jaroslav (Discussiones Mathematicae Graph Theory, 2016)
An edge coloring φ of a graph G is called an M2-edge coloring if |φ(v)| ≤ 2 for every vertex v of G, where φ(v) is the set of colors of edges incident with v. Let 𝒦2(G) denote the maximum number of colors used in an M2-edge coloring of G. In this paper we determine 𝒦2(G) for trees, cacti, complete multipartite graphs and graph joins.