A new sufficient condition for graphs of f-class 1

An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex nu is an element of V(C) at most (nu) times. The minimum number of colors needed to f-color G is called the f-chromatic index of C. A simple graph G is of f-class 1 if the f-chromatic index of G equals Delta(f) (G), where Delta(f)(G) = maac(nu eV(G)){[d(nu)/f(nu])}. In this article, we find a new sufficient condition for a simple graph to be of f-class 1, which is strictly better than a condition presented by Zhang and Liu in 2008 and is sharp. Combining the previous conclusions with this new condition, we improve a result of Zhang and Liu in 2007.