ZDP(n) ${Z}_{DP}(n)$ is bounded above by n2−(n+3)∕2 ${n}^{2}-(n+3)\unicode{x02215}2$

Abstract

AbstractIn 2018, Dvořák and Postle introduced a generalization of proper coloring, the so‐called DP‐coloring. For any graph , the DP‐chromatic number of is defined analogously with the chromatic number of . In this article, we show that holds for , where is the join of and a complete graph with vertices. As a result, holds for every integer , where is the minimum nonnegative integer such that holds for every graph with vertices. Our result improves the best current upper bound of due to Bernshteyn, Kostochka, and Zhu.