A note on the edge cover chromatic index of multigraphs

Let G be a multigraph with vertex set V(G). An edge coloring C of G is called an edge-cover-coloring if each color appears at least once at each vertex [email protected]?V(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 @g"c^'(G). It is well known that min{d(v)[email protected](v):[email protected]?V}@[email protected]"c^'(G)@[email protected](G), where @m(v) is the multiplicity of v and @d(G) is the minimum degree of G. We improve this lower bound to @d(G)-1 when [email protected][email protected](G)@?5. Furthermore we show that this lower bound is best possible.