Abstract
An fg-coloring of a multigraph is a coloring of edges such that each color appears at each vertex v at most f(v) times and at each set of multiple edges joining vertices v and w at most g(vw) times. The minimum number of colors needed to fg-color a multigraph is called the fg-chromatic index of the multigraph. This paper proves a new upper bound on the fg-chromatic index. The proof immediately yields a polynomial time algorithm to fg-color a given multigraph using a number of colors not exceeding the upper bound. The worst-case ration of the algorithm is at most 3/2.
