2025/03/19 by Cui, Ruiyi, Wan, Liangxia, Dong, Fengming
#05C15 #05C30 #05C65 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.14879
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.