List Supermodular Coloring with Shorter Lists

Abstract

In 1995, Galvin proved that a bipartite graph G admits a list edge coloring if every edge is assigned a color list of length Δ(G) the maximum degree of the graph. This result was improved by Borodin, Kostochka and Woodall, who proved that G still admits a list edge coloring if every edge e=st is assigned a list of max{dG(s);dG(t)} colors. Recently, Iwata and Yokoi provided the list supermodular coloring theorem that extends Galvin's result to the setting of Schrijver's supermodular coloring. This paper provides a common generalization of these two extensions of Galvin's result.

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Correspondence to Yu Yokoi.

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Yokoi, Y. List Supermodular Coloring with Shorter Lists. Combinatorica 39, 459–475 (2019). https://doi.org/10.1007/s00493-018-3830-1

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Mathematics Subject Classification (2010)

  • 05C15
  • 68R05