A note on the edge cover chromatic index of multigraphs |
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Authors: | Changqing Xu Guizhen Liu |
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Institution: | a Department of Applied Mathematics, Hebei University of Technology, Tianjin 300401, PR China b Department of Mathematics, Shandong University, Jinan, Shandong, 250100, PR China |
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Abstract: | 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 v∈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 . It is well known that , where μ(v) is the multiplicity of v and δ(G) is the minimum degree of G. We improve this lower bound to δ(G)−1 when 2≤δ(G)≤5. Furthermore we show that this lower bound is best possible. |
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Keywords: | Edge-cover-coloring Edge cover chromatic index |
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