Abstract
Let G be a graph and suppose that for each vertex v of G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k-list colorable graph. M. Ghebleh and E. S. Mahmoodian characterized uniquely 3-List colorable complete multipartite graphs except for nine graphs. Recently, except for graph K 2,3,4, the other eight graphs were shown not to be uniquely 3-list colorable by W. He and Y. Shen, etc. In this paper, it is proved that K 2,3,4 is not uniquely 3-list colorable, and then the uniquely 3-list colorable complete multipartite graphs are characterized completely.
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Zhao, Y., He, W., Shen, Y., Wang, Y. (2007). Note on Characterization of Uniquely 3-List Colorable Complete Multipartite Graphs. In: Akiyama, J., Chen, W.Y.C., Kano, M., Li, X., Yu, Q. (eds) Discrete Geometry, Combinatorics and Graph Theory. CJCDGCGT 2005. Lecture Notes in Computer Science, vol 4381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70666-3_30
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DOI: https://doi.org/10.1007/978-3-540-70666-3_30
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