Some orientation theorems for restricted DP-colorings of graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913616792387584 |
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| author | Gossett, Ian |
| author_facet | Gossett, Ian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12706 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some orientation theorems for restricted DP-colorings of graphs Gossett, Ian Combinatorics 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. |
| title | Some orientation theorems for restricted DP-colorings of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2308.12706 |