Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six
Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six
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DOI：
10.7151/dmgt.1556
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Y. Bu;Ko-Wei Lih;Weifan Wang
中科院分区：
文献类型：
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作者：
Y. Bu;Ko-Wei Lih;Weifan Wang
图G的相邻顶点可区分边着色是图G的适当边着色，使得任意对相邻顶点都关联于不同的颜色集。相邻顶点区分G的边缘着色所需的最小颜色数用χ’a (G)表示。证明了如果G是一个周长至少为6的无孤立边的平面图，则χ ' a (G)不超过最大度+ 2。这为《科学》中提出的一个猜想提供了新的证据
An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ ′ a (G). We prove that χ ′ a (G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in