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On Non 3-Choosable Bipartite Graphs

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Computational Geometry and Graphs (TJJCCGG 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8296))

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Abstract

In 2003, Fitzpatrick and MacGillivray proved that every complete bipartite graph with fourteen vertices except K 7,7 is 3-choosable and there is the unique 3-list assignment L up to renaming the colors such that K 7,7 is not L-colorable. We present our strategies which can be applied to obtain another proof of their result. These strategies are invented to claim a stronger result that every complete bipartite graph with fifteen vertices except K 7,8 is 3-choosable. We also show all 3-list assignments L such that K 7,8 is not L-colorable.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand

    W. Charoenpanitseri & C. Uiyyasathian

  2. Department of Mathematics, Srinakharinwirot University, Sukhumvit 23, Bangkok, 10110, Thailand

    N. Punnim

Authors
  1. W. Charoenpanitseri
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  2. N. Punnim
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  3. C. Uiyyasathian
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Editor information

Editors and Affiliations

  1. Research Center for Math and Science Education, Tokyo University of Science, 1-3 Kagurazaki, 162-8601, Shinjuku, Tokyo, Japan

    Jin Akiyama

  2. Department of Computer and Information Science, Ibaraki University, Hitachi, Ibaraki, Japan

    Mikio Kano

  3. Research Institute of Educational Development, Tokai University, Tomigaya, Shibuya-ku, Tokyo, Japan

    Toshinori Sakai

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Charoenpanitseri, W., Punnim, N., Uiyyasathian, C. (2013). On Non 3-Choosable Bipartite Graphs. In: Akiyama, J., Kano, M., Sakai, T. (eds) Computational Geometry and Graphs. TJJCCGG 2012. Lecture Notes in Computer Science, vol 8296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45281-9_4

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  • DOI: https://doi.org/10.1007/978-3-642-45281-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45280-2

  • Online ISBN: 978-3-642-45281-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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