A NOTE ON EDGE-COVER COLORING OF NEARLY BIPARTITE GRAPHS

Let G be a graph with vertex set V(G). An edge coloring C of G is called an edge-cover coloring, if for each color, the edges assigned with it forms an edge cover of G. The maximum positive integer k such that G has a k-edge-cover coloring is called the edge cover chromatic index of G and is denoted by chi'(c)(G). It is well known that min{d(v) - mu(v) : v is an element of V} <= chi'(c)(G) <= delta(G), where mu(v) is the multiplicity of v and 6(G) is the minimum degree of G. If chi'(c)(G) = delta(G), G is called a graph of CI class, otherwise G is called a graph of CII class. In this paper, we give a new sufficient condition for a nearly bipartite graph to be of CI class.