Abstract:

An edge cover-coloring of a graph G is called a super f-edge cover-coloring, if each color appears at each vertex v at least f(v) times and multiple edges
receive different colors. Let χ^H_fc denote the maximum positive integer k for which by using k colors a super f-edge cover-coloring of G exists. The existence of χ^H_fc is discussed and its lower bound is obtained.

Key words: Multigraph, f-edge cover-coloring, Super f-edge cover-coloring, Exchange chain, Obstruction