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arXiv · 2308.12706

Some orientation theorems for restricted DP-colorings of graphs

Ian Gossett
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Abstract

We define $Z$-signable correspondence assignments on multigraphs, which generalize good correspondence assignments as introduced by Kaul and Mudrock. We introduce an auxiliary digraph that allows us to prove an Alon-Tarsi style theorem for DP-colorings from $Z$-signable correspondence assignments on multigraphs, and apply this theorem to obtain three DP-coloring analogs of the Alon-Tarsi theorem for arbitrary correspondence assignments as corollaries. We illustrate the use of these corollaries for DP-colorings on a restricted class of correspondence assignments on toroidal grids.

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Ian Gossett. 2023-08-24. Some orientation theorems for restricted DP-colorings of graphs. https://doi.org/10.1016/j.disc.2024.114352

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