If a graph admits a -list assignment such that has a unique -coloring, then is called uniquely -list colorable graph, or ULC graph for short. In the process of characterizing ULC 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 ULC, which provide a very significant guide for constructing such list assignment. Then a special example of ULC graphs as a application of these propositions is introduced. The conclusion will pave the way to characterize ULC complete multipartite graphs.
"Some Conclusion on Unique -List Colorable Complete Multipartite Graphs." J. Appl. Math. 2013 1 - 5, 2013. https://doi.org/10.1155/2013/380861