摘要

A (g, f)-coloring 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 nonnegative and positive integers assigned to v, respectively. The minimum number of colors used by a (g, f)-coloring of G is called the (g, f)-chromatic index of G. The maximum number of colors used by a (g, f)-coloring of G is called the upper (g, f)-chromatic index of G. In this paper, we determine the (g, f)-chromatic index and the upper (g, f)-chromatic index in some cases.