DP color functions of hypergraphs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912282492010496 |
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| author | Cui, Ruiyi Wan, Liangxia Dong, Fengming |
| author_facet | Cui, Ruiyi Wan, Liangxia Dong, Fengming |
| contents | In this article, we introduce the DP color function of a hypergraph, based on the DP coloring introduced by Bernshteyn and Kostochka, which is the minimum value where the minimum is taken over all its k-fold covers. It is an extension of its chromatic polynomial. we obtain an upper bound for the DP color functions of hypergraphs when hypergraphs are connected r-uniform hypergraphs for any r greater than one. The upper bound is attained if and only if the hypergraph is a r-uniform hypertree. We also show the cases of the DP color function equal to its chromatic polynomial. These conclusions coincide with the known results of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | DP color functions of hypergraphs Cui, Ruiyi Wan, Liangxia Dong, Fengming Combinatorics 05C15, 05C30, 05C65 In this article, we introduce the DP color function of a hypergraph, based on the DP coloring introduced by Bernshteyn and Kostochka, which is the minimum value where the minimum is taken over all its k-fold covers. It is an extension of its chromatic polynomial. we obtain an upper bound for the DP color functions of hypergraphs when hypergraphs are connected r-uniform hypergraphs for any r greater than one. The upper bound is attained if and only if the hypergraph is a r-uniform hypertree. We also show the cases of the DP color function equal to its chromatic polynomial. These conclusions coincide with the known results of graphs. |
| title | DP color functions of hypergraphs |
| topic | Combinatorics 05C15, 05C30, 05C65 |
| url | https://arxiv.org/abs/2503.14879 |