On characterization of uniquely 3-list colorable complete multipartite graphs

• Autorzy: Yancai Zhao , Erfang Shan
• Języki publikacji: EN

Abstrakty

EN

For each vertex v of a graph G, if 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. Ghebleh and Mahmoodian characterized uniquely 3-list colorable complete multipartite graphs except for nine graphs: $K_{2,2,r}$ r ∈ {4,5,6,7,8}, $K_{2,3,4}$, $K_{1*4,4}$, $K_{1*4,5}$, $K_{1*5,4}$. Also, they conjectured that the nine graphs are not U3LC graphs. After that, except for $K_{2,2,r}$ r ∈ {4,5,6,7,8}, the others have been proved not to be U3LC graphs. In this paper we first prove that $K_{2,2,8}$ is not U3LC graph, and thus as a direct corollary, $K_{2,2,r}$ (r = 4,5,6,7,8) are not U3LC graphs, and then the uniquely 3-list colorable complete multipartite graphs are characterized completely.

Słowa kluczowe

EN

list coloring; complete multipartite graph; uniquely 3-list colorable graph

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 1
• Strony: 105-114

Daty

wydano

2010

otrzymano

2009-02-26

poprawiono

2009-04-02

zaakceptowano

2009-04-14

Twórcy

autor

Yancai Zhao

• Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
• Department of Science, Bengbu University, Anhui 233030, P.R. China

autor

Erfang Shan

• Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China

Bibliografia

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• [8] M. Mahdian and E.S. Mahmoodian, A characterization of uniquely 2-list colorable graphs, Ars Combin. 51 (1999) 295-305.
• [9] E.S. Mahmoodian and M. Mahdian, On the uniquely list colorable graphs, in: Proceedings of the 28th Annual Iranian Mathematics Conference, Part 1, number 377 in Tabriz Univ. Ser., Tabriz, 1997.
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• [12] Y.Q. Zhao, W.J. He, Y.F. Shen and Y.N. Wang, Note on characterization of uniquely 3-list colorable complete multipartite graphs, in: Discrete Geometry, Combinatorics and Graph Theory, LNCS 4381 (Springer, Berlin, 2007) 278-287, doi: 10.1007/978-3-540-70666-3₃0.

Identyfikatory

DOI

10.7151/dmgt.1480