论文标题:完全三部图K_（2，2，r）（r=4，5，6）具有M（3）性质
The Complete Tripartite Graphs K_(2,2,r)(r=4,5,6) Have Property M(3)
论文作者 马新苗
论文导师 何文杰,论文学位 硕士,论文专业 应用数学
论文单位 河北工业大学,点击次数 94,论文页数 33页File Size918k
2005-05-01论文网 http://www.lw23.com/lunwen_910543777/ 列表染色;ukLC图;M(3)性质;K_(2、2、r)
list coloring; uniquely k-list colorable graph; K_(2、2、r);property M(3)
列表染色这个概念最初由V.G.Vizing,P.Erdos,A.L.Rubin和H.Taylor独立的提出来的。近年来,人们对该领域进行了大量的研究和探索,并取得了不少成果,同时仍存在许多待解决的问题。关于唯一列表染色,E.s.Mahmoodian和M.Mahdian特征化了绝大部分完全多部图,本文就E.S.Mahmoodian和M.Mahdian提出来的开放问题作出了部分解决。首先系统地总结了唯一列表染色图的研究成果和研究进展,然后我们叙述并证明了完全三部图K_(2,2,r)(r=4,5,6) 不是U3LC图,且它的m数是3. 此结论扩充完善了E.S.Mahmoodian和M.Mahdian的结论。
The idea of list coloring of graphs is independently due to V. G. Vizing and to P. Erdos, A. L. Rubin, and H. Taylor. This is an interesting definition in graph theory. Plenty of rearch and exploration has been done in this field in the last years. Many achievements have been gained. Meanwhile, a considerable number of unsolved problems have been remained. On uniquely k-list colorable graphs, M. Ghebleh and E. S. Mahmoodian have characterized almost all uniquely 3-list colorable complete multipartite graphs. In this paper, we partially solve the open problem which is introduced by M. Ghebleh and E. S. Mahmoodian. Firstly we will systematically summarize the results of the research of uniquely A;-list colorable graphs. Then we will fully detail that K2,2,r{r = 4,5,6) have property M(3). The result improves the preceding result.
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