DP color functions of hypergraphs
Combinatorics
2025-03-20 v1
Abstract
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.
Cite
@article{arxiv.2503.14879,
title = {DP color functions of hypergraphs},
author = {Ruiyi Cui and Liangxia Wan and Fengming Dong},
journal= {arXiv preprint arXiv:2503.14879},
year = {2025}
}