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2013 Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs
Yanning Wang, Yanyan Wang, Xuguang Zhang
J. Appl. Math. 2013: 1-5 (2013). DOI: 10.1155/2013/380861

Abstract

If a graph G admits a k-list assignment L such that G has a unique L-coloring, then G is called uniquely k-list colorable graph, or UkLC graph for short. In the process of characterizing UkLC graphs, the complete multipartite graphs K1*r,s(r,sN) are often researched. But it is usually not easy to construct the unique k-list assignment of K1*r,s. In this paper, we give some propositions about the property of the graph K1*r,s when it is UkLC, which provide a very significant guide for constructing such list assignment. Then a special example of UkLC graphs K1*r,s as a application of these propositions is introduced. The conclusion will pave the way to characterize UkLC complete multipartite graphs.

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Yanning Wang. Yanyan Wang. Xuguang Zhang. "Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs." J. Appl. Math. 2013 1 - 5, 2013. https://doi.org/10.1155/2013/380861

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950641
MathSciNet: MR3115283
Digital Object Identifier: 10.1155/2013/380861

Rights: Copyright © 2013 Hindawi

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