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Some Conclusion on Unique k‐List Colorable Complete Multipartite Graphs

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  • Yanning Wang
  • Yanyan Wang
  • Xuguang Zhang

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, s ∈ N) 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.

Suggested Citation

  • Yanning Wang & Yanyan Wang & Xuguang Zhang, 2013. "Some Conclusion on Unique k‐List Colorable Complete Multipartite Graphs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:380861
    DOI: 10.1155/2013/380861
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