On the Upper Chromatic Index of a Multigraph
Mario Gionfriddo, Lorenzo Milazzo, Vitaly Voloshin · 2001
We consider the colorings of the edges of a multigraph in such a way that every non-pendant vertex is incident to at least two edges of the same color. We prove that the upper chromatic index is equal to c+m-n+p where c is the maximum number of vertex disjoint cycles, m,n and p are the numbers of edges, vertices and pendant vertices of a multigraph.