Extensions of Galvin's Theorem
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Date
2018-04-30
Authors
Levit, Maxwell
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Publisher
University of Waterloo
Abstract
We discuss problems in list coloring with an emphasis on techniques that utilize oriented graphs. Our central theme is Galvin's resolution of the Dinitz problem (Galvin. J. Comb. Theory, Ser. B 63(1), 1995, 153--158).
We survey the related work of Alon and Tarsi (Combinatorica 12(2) 1992, 125--134) and H\"{a}ggkvist and Janssen (Combinatorics, Probability \& Computing 6(3) 1997,
295--313). We then prove two new extensions of Galvin's theorem.
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Keywords
Graph Coloring, List Coloring, Galvin's Theorem