On the vertex face total chromatic number of planar graphs
On the vertex face total chromatic number of planar graphs
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DOI：
10.1002/(sici)1097-0118(199605)22:1
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
Weifan Wang;Jiazhuang Liu
中科院分区：
文献类型：
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作者：
Weifan Wang;Jiazhuang Liu
设\(G\)是一个平面图。\(G\)的顶点面全色数\(\chi_{vf}(G)\)是对\(V(G)\cup F(G)\)进行着色时所需的最少颜色数，使得相邻或相关联的元素不会被赋予相同的颜色。本文的主要结果如下：（1）我们给出了所有外平面图以及模\(3\) - 正则极大平面图的顶点面全色数。（2）我们证明了如果\(G\)是一个极大平面图或者一个低度平面图，即\(\Delta(G)\leq3\)，那么\(\chi_{vf}(G)\leq6\)。
Let G be a planar graph. The vertex face total chromatic number ,y13(G) of G is the least number of colors assigned to V(G) U F(G) such that no adjacent or incident elements receive the same color. The main results of this paper are as follows: (1) We give the vertex face total chromatic number for all outerplanar graphs and modulus 3-regular maximal planar graphs. (2) We prove that if G is a maximal planar graph or a lower degree planar graph, i.e., A(G) 5 3, then ,y13(G) 5 6.