Sparse critical graphs for defective DP-colorings
Alexandr V. Kostochka, Jingwei Xu · Discrete Mathematics · 2024
An interesting generalization of list coloring is so called DP-coloring (named after Dvořák and Postle). We study (i,j)-defective DP-colorings of simple graphs. Define gDP(i,j,n) to be the minimum number of edges in an n-vertex DP-(i,j)-critical graph. We prove sharp bounds on gDP(i,j,n) for i=1,2 and j≥2i for infinitely many n.