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Note on Characterization of Uniquely 3-List Colorable Complete Multipartite Graphs

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Discrete Geometry, Combinatorics and Graph Theory (CJCDGCGT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4381))

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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Authors and Affiliations

  1. Department of Mathematics, Shijiazhuang College, Shijiazhuang 050035, P.R. China

    Yongqiang Zhao

  2. Applied Mathematics Institute, Hebei University of Technology, Tianjin 300130, P.R. China

    Wenjie He

  3. Department of Mathematics and Physics, Hebei Normal University of Science and Technology, Qinhuangdao 066004, P.R. China

    Yufa Shen

  4. Department of Mathematics, Yanshan University, Qinhuangdao 066004, P.R. China

    Yanning Wang

Authors
  1. Yongqiang Zhao
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  2. Wenjie He
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  3. Yufa Shen
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  4. Yanning Wang
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Jin Akiyama William Y. C. Chen Mikio Kano Xueliang Li Qinglin Yu

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© 2007 Springer Berlin Heidelberg

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70665-6

  • Online ISBN: 978-3-540-70666-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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