Liu Guizhen

The edge-coloring problem was posed in relation with the well-known four-color conjecture. Vizing proved the famous Vizing's theorem. Hakimi et al. studied the f-coloring problem. In 1990, Nakano et al. studied the fg-coloring problem. The edge cover coloring of a graph G is to color all the edges of G so that each color appears at each vertex v at least one times. The maximum positive integer k such that G has a k-edge cover-coloring is called the edge cover chromatic index of G .The (g, f )-coloring is a generalization of edge-coloring and edge cover coloring. In this paper some results on edge cover colorings, G-edge cover colorings, (g, f )-colorings and equitable edge colorings are introduced. In particular, some new results on the above colorings obtained by us are presented. Moreover some open problems are also presented.