Jingwei Xu (UIUC)
Sparse critical graphs for defective DP-colorings
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Abstract: DP-coloring, named after Dvořák and Postle, is an interesting generalization of list coloring. We study (i, j)-defective DP-colorings of simple graphs. Let g_{DP}(i, j, n) be the minimum number of edges in an n-vertex DP-(i, j)-critical graph. We give sharp bound on g_{DP}(i, j, n) for i=1, 2 and j\geq 2i for infinitely many n. This is joint work with Alexandr Kostochka.
