Extensions of Galvin's Theorem
Maxwell Levit · UWSpace (University of Waterloo) · 2018
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.