Adjacent vertex distinguishing total coloring of planar graphs with large maximum degree
Adjacent vertex distinguishing total coloring of planar graphs with large maximum degree
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DOI：
10.1360/012011-359
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发表时间：
2012-02
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影响因子：
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通讯作者：
Danjun Huang;Weifan Wang
中科院分区：
文献类型：
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作者：
Danjun Huang;Weifan Wang
图\(G\)的一个邻点可区别全染色是\(G\)的一个正常全染色，使得任意一对相邻顶点所关联的颜色集合不同。\(G\)的邻点可区别全染色所需的最少颜色数用\(\chi_{a}''(G)\)表示。在本文中，我们证明了对于每一个最大度\(\Delta(G)\geq11\)的平面图\(G\)，都有\(\chi_{a}''(G)\leq\Delta(G)+3\)。
An adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors needed for an adjacent vertex distinguishing total coloring of G is denoted by χ a ′′( G ). In this paper, we prove that every planar graph G with Δ( G ) ≥ 11 has χ a ′′( G ) ≤ Δ( G ) + 3.