Let G be a multigraph with vertex set V（G）. Assume that a positive integer f（v） with 1 ≤ f（v） ≤ d（v） is associated with each vertex v ∈ V. An edge coloring of G is called an f-edge cover-coloring, if each c...Let G be a multigraph with vertex set V（G）. Assume that a positive integer f（v） with 1 ≤ f（v） ≤ d（v） is associated with each vertex v ∈ V. An edge coloring of G is called an f-edge cover-coloring, if each color appears at each vertex v at least f（v） times. Let X＇fc（G） be the maximum positive integer k for which an f-edge cover-coloring with k colors of G exists. In this paper, we give a new lower bound of X＇fc（G）, which is sharp.展开更多
文摘Let G be a multigraph with vertex set V（G）. Assume that a positive integer f（v） with 1 ≤ f（v） ≤ d（v） is associated with each vertex v ∈ V. An edge coloring of G is called an f-edge cover-coloring, if each color appears at each vertex v at least f（v） times. Let X＇fc（G） be the maximum positive integer k for which an f-edge cover-coloring with k colors of G exists. In this paper, we give a new lower bound of X＇fc（G）, which is sharp.
