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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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
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