List Supermodular Coloring with Shorter Lists
Yu Yokoi

TL;DR
This paper generalizes key results in list edge coloring of bipartite graphs by extending theorems from Galvin, Borodin-Kostochka-Woodall, and Iwata-Yokoi to a broader supermodular coloring framework.
Contribution
It introduces a unified theorem that encompasses previous list coloring results for bipartite graphs and supermodular coloring, advancing the theoretical understanding.
Findings
Generalizes Galvin's list edge coloring theorem
Extends Borodin-Kostochka-Woodall's bounds to supermodular setting
Provides a unified framework for bipartite list coloring and supermodular coloring
Abstract
In 1995, Galvin proved that a bipartite graph admits a list edge coloring if every edge is assigned a color list of length , the maximum degree of the graph. This result was improved by Borodin, Kostochka and Woodall, who proved that still admits a list edge coloring if every edge is assigned a list of 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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