| 唯一3-列表可染图Kr,s,t和K1*r,s的若干性质 |
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| 引用本文： | 申玉发,郑国萍,王艳宁,何文杰.唯一3-列表可染图Kr,s,t和K1*r,s的若干性质[J].河北科技师范学院学报,2005,19(4):42-45. |
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| 作者姓名： | 申玉发 郑国萍 王艳宁 何文杰 |
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| 作者单位： | 河北科技师范学院,数理系,河北,秦皇岛,066004;河北师范大学;河北科技师范学院,数理系,河北,秦皇岛,066004;燕山大学;河北工业大学 |
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| 基金项目： | 河北省教育厅自然科学研究项目(项目编号:2005008). |
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| 摘 要： | 2001年Ghebleh M和Mahmoodian E S针对完全多部图这一重要图类（除了其中9个图），特征化了U3LC图。同时他们对这9个图提出了开放问题：查证图K（2,2,r）,r=4，5，6，7，8，K（2,3,4）.K（1＊4,4）,K（1＊4,5）和K（1＊5,4）不是U3LC图。鉴于此开放问题中待查证的图或是完全三部图K（r,s,t）或是完全多部图K（1＊r,s），笔者从反面入手研究U3LC完全三部图K（r,s,t）和完全多部图K（1＊r,s）的性质，以期实现最终利用这些性质彻底解决如上开放问题，完善Ghebleh M和Mahmoodian E S的结果。
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| 关 键 词： | 完全多部图 Kr s t和K1*r 列表染色 唯一3-列表可染图 |
| 文章编号： | 1672-7983(2005)04-0042-04 |
| 修稿时间： | 2005年3月18日 |
Some Properties on Uniquely 3-List Colorable Graphs Kr,s,t and K1*r,s |
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| SHEN Yu-fa,ZHENG Guo-ping,WANG Yan-ning,HE Wen-jie.Some Properties on Uniquely 3-List Colorable Graphs Kr,s,t and K1*r,s[J].Journal of Hebei Normal University of Science & Technology,2005,19(4):42-45. |
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| Authors: | SHEN Yu-fa ZHENG Guo-ping WANG Yan-ning HE Wen-jie |
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| Abstract: | In 2001, Ghebleh M and Mahmoodian E S characterized U3LC graphs for complete multipartite graphs, which is an important class of graphs, with nine supplementary graphs that present here an open problem ( to verify the graphs K2,2,r,r=4,5,6,7,8,K2,3,4 ,K1,4,4,K1*5,4 and K1*5,4 not being U3LC graphs). Since any graph that needs to be verified is either a complete tripartite graph Kr,s,t or complete multipartite graph K1*r,s, some properties of U3LC graphs Kr,s,t and K1*r,s which are at variance to them, have been discussed in this paper. We hope that the above open problem can be resolved completely by using the properties in this paper,and the result of Ghebleh M and Mahmoodian E S can be measurably improved. |
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| Keywords: | Complete multipartite graph K_(r s t) and K_(1*r s) List coloring Uniquely 3-list colorable graph |
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