A note on the edge cover chromatic index of multigraphs
A note on the edge cover chromatic index of multigraphs
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DOI：
10.1016/j.disc.2007.11.049
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发表时间：
2008-12
期刊：
影响因子：
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通讯作者：
Changqing Xu;G. Liu
中科院分区：
文献类型：
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作者：
Changqing Xu;G. Liu
设G是一个顶点集为V（G）的重图. G的边染色C称为边覆盖染色，如果每种颜色在每个顶点v∈V（G）上至少出现一次.使G有k-边覆盖染色的最大正整数k称为G的边覆盖色数，记为χc′（G）.已知min{d（v）−μ（v）：v∈V}≤χc′（G）≤δ（G），其中μ（v）是v的重数，δ（G）是G的最小度.当2≤δ（G）≤5时，我们将这个下界改进为δ（G）−1。此外，我们表明，这个下界是最好的可能。
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 χc′(G). It is well known that min{d(v)−μ(v):v∈V}≤χc′(G)≤δ(G), 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.