| Heawood反例图的全部四着色 |
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| 引用本文： | 许寿椿,程斌,杨宁,宝力高,丁保岭.Heawood反例图的全部四着色[J].中央民族大学学报(自然科学版),2007,16(4):299-303. |
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| 作者姓名： | 许寿椿 程斌 杨宁 宝力高 丁保岭 |
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| 作者单位： | 中央民族大学,理学院,北京,100081 |
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| 摘 要： | 本文首次报告了Heawood反例图的全部四着色.它可以用一个树林来描述.树林的每个分支是一棵四着色树.四着色树是一个根树.根节点Cr是Heawood反例图的一个四着色.根树其它节点都是经过一个或多个二色变换从Cr变来的.Heawood反例图有37个四着色树.其中有35个偶四色树(包括24个是仅有根结点的退化型四色树),2个奇四色树.偶四着色总计112,奇四着色总计144,全部四着色总共256个.这些结果都是用Maple编程得到的.
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| 关 键 词： | 四着色算法 极大平面图 色多项式 四色不变量 |
| 文章编号： | 1005-8036（2007）04-0299-05 |
| 修稿时间： | 2007-06-25 |
All 4-Colorpings of Heawood's Counterexample |
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| XU Shou-chun,CHENG Bin,YANG Ning,BAO Li-gao,DING Bao-ling.All 4-Colorpings of Heawood''''s Counterexample[J].Journal of The Central University for Nationalities(Natural Sciences Edition),2007,16(4):299-303. |
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| Authors: | XU Shou-chun CHENG Bin YANG Ning BAO Li-gao DING Bao-ling |
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| Institution: | College of Science, Central University for Nationalities, Beijing 100081, China |
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| Abstract: | In this paper all of 4-colorpings of Heawood's counterexample are given.It can be described by a forest.Each component of the forest is a Tfc(Tree of 4-colorings).The Tfc is a rooted tree.The rooted note is a 4-colopings of Heawood's counterexample,Cr.Each of other notes is induced by a Kempe's interchange or some Kempe's interchanges from Cr.The Heawood's counterexample graph has 37 trees of 4-colorings.In where there are 35 even Tfc and 2 odd Tfc.The Heawood's counterexample graph has 112 even 4-colorings and 144 odd 4-colorings. |
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| Keywords: | 4-coloring algorithm Maximal planar graph Chromatic polynomial |
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