A note on the (g,f)-coloring

In an ordinary edge-coloring of a graph, each color appears at each vertex v at most once. A (g,f)-coloring (factorization) is a generalized edge-coloring in which each color appears at each vertex v at least g(v) and at most f(v) times, where g(v) and f(v) are respectively nonnegative and positive integers assigned to v. Using coloring method, we give a new necessary and sufficient condition for a bipartite graph to have a (g,f)-coloring and we give some sufficient conditions for a general graph to have a (g,f)-coloring. © 2008 Korean Society for Computational and Applied Mathematics.