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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 380861, 5 pages
Research Article

Some Conclusion on Unique -List Colorable Complete Multipartite Graphs

1School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, China
2Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China
3School of Economics and Management, Yanshan University, Qinhuangdao, Hebei 066004, China

Received 6 March 2013; Revised 4 September 2013; Accepted 11 September 2013

Academic Editor: Huijun Gao

Copyright © 2013 Yanning Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


If a graph admits a -list assignment such that has a unique -coloring, then is called uniquely -list colorable graph, or U LC graph for short. In the process of characterizing U LC graphs, the complete multipartite graphs are often researched. But it is usually not easy to construct the unique -list assignment of . In this paper, we give some propositions about the property of the graph when it is U LC, which provide a very significant guide for constructing such list assignment. Then a special example of U LC graphs as a application of these propositions is introduced. The conclusion will pave the way to characterize U LC complete multipartite graphs.