Abstract
Given a multigraph G, an edge cover-coloring of G is called an f-edge cover-coloring, if each color appears at each vertex v at least f(v) times. Let [Formula: see text] be the maximum positive integer k for which an f-edge cover-coloring with k colors of G exists. An f-edge cover-coloring of G is called a super f-edge cover-coloring, if parallel edges receive distinct colors. Let [Formula: see text] denote the maximum positive integer k for which a super f-edge cover-coloring with k colors of G exists. A sufficient condition for a graph G to have [Formula: see text] is given.
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