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Some Conclusion on Unique -List Colorable Complete Multipartite Graphs

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  • Yanning Wang
  • Yanyan Wang
  • Xuguang Zhang

Abstract

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.

Suggested Citation

  • Yanning Wang & Yanyan Wang & Xuguang Zhang, 2013. "Some Conclusion on Unique -List Colorable Complete Multipartite Graphs," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, October.
    • Handle: RePEc:hin:jnljam:380861
    DOI: 10.1155/2013/380861
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