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math.CO2023
Sparse critical graphs for defective -coloring
Alexandr Kostochka, Jingwei Xu, Xuding Zhu
A graph is -colorable if its vertices can be partitioned into subsets and so that every vertex in has degree at most and every vertex in $G[V_2]…
math.CO2023
Injective edge colorings of degenerate graphs and the oriented chromatic number
Peter Bradshaw, Alexander Clow, Jingwei Xu
Given a graph , an injective edge-coloring of is a function such that if , then no third edge joins an endpoint of and an en…
math.CO2023
Sparse critical graphs for defective DP-colorings
Alexandr Kostochka, Jingwei Xu
An interesting generalization of list coloring is so called DP-coloring (named after Dvořák and Postle). We study -defective DP-colorings of simple graphs. Define $g_{DP}(i,…