ZDP (n) is bounded above by n2 −(n+3) / 2

In 2018, Dvořák and Postle introduced a generalization of proper coloring, the so-called DP-coloring. For any graph (Figure presented.), the DP-chromatic number (Figure presented.) of (Figure presented.) is defined analogously with the chromatic number (Figure presented.) of (Figure presented.). In this article, we show that (Figure presented.) holds for (Figure presented.), where (Figure presented.) is the join of (Figure presented.) and a complete graph with (Figure presented.) vertices. As a result, (Figure presented.) holds for every integer (Figure presented.), where (Figure presented.) is the minimum nonnegative integer (Figure presented.) such that (Figure presented.) holds for every graph (Figure presented.) with (Figure presented.) vertices. Our result improves the best current upper bound (Figure presented.) of (Figure presented.) due to Bernshteyn, Kostochka, and Zhu. © 2023 Wiley Periodicals LLC.