| 系列平行图的边面染色 |
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| 引用本文： | 吴建良,WANG Ping.系列平行图的边面染色[J].数学进展,2005,34(4):461-467. |
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| 作者姓名： | 吴建良 WANG Ping |
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| 作者单位： | 1. 山东大学数学学院,济南,山东,250100
2. Dept.of Mathematics Statistics and Computer Science,St.Francis Xavier University,Antigonish,NS,Canada B2G 2W5 |
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| 基金项目： | This work was partially supported by National Natural Science Foundation of China(No. 10471078)
Doctoral Foundation of the Education committee of China(No. 2004042204)
Supported by an NSERC grant Canada |
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| 摘 要： | 一个平面图G的边面色数xef(G)是指对G的边和面进行染色所用最少的颜色数目,并同时使得相邻或相关联的两个元素间染不同颜色.若G是一个系列平行图,也就是不含K_4的剖分作为子图的平面图,则有Xef(G)≤max{7,△(G) 1};同时如果G还是2-连通的且△(G)>6,则有Xef(G)=△.
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| 关 键 词： | 图 系列平行图 边面色数 |
| 文章编号： | 1000-0917（2005）04-0461-07 |
| 收稿时间： | 2002-12-27 |
| 修稿时间： | 2005-02-12 |
Simultaneous Coloring of Edges and Faces of Series-parallel Graphs |
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| WU Jian-Liang,WANG Ping.Simultaneous Coloring of Edges and Faces of Series-parallel Graphs[J].Advances in Mathematics,2005,34(4):461-467. |
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| Authors: | WU Jian-Liang WANG Ping |
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| Abstract: | The edge-face chromatic number χef(G) of a plane graph G is the minimal number of colors needed for coloring edges and faces of G such that no two adjacent or incident elements receive the same color. Here it is proved that for any series-parallel graph G, that is, a plane graph which contains no subgraphs homeomorphic to K4, χef(G) ≤ max{7,△(G) + 1}; Moreover,χef(G) = △ if G is 2-connected and △(G) ≥ 6. |
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| Keywords: | series-parallel graph edge-face chromatic number coloring |
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