Sparse critical graphs for defective DP-colorings

Alexandr Kostochka; Jingwei Xu

Sparse critical graphs for defective DP-colorings

Combinatorics 2023-06-27 v1

Authors: Alexandr Kostochka , Jingwei Xu

Abstract

An interesting generalization of list coloring is so called DP-coloring (named after Dvo\v{r}\'ak and Postle). We study $(i,j)$ -defective DP-colorings of simple graphs. Define $g_{DP}(i,j,n)$ to be the minimum number of edges in an $n$ -vertex DP- $(i,j)$ -critical graph. We prove sharp bounds on $g_{DP}(i,j,n)$ for $i=1,2$ and $j\geq 2i$ for infinitely many $n$ .

Keywords

graph coloring graph pebbling graph theory

Cite

@article{arxiv.2306.14295,
  title  = {Sparse critical graphs for defective DP-colorings},
  author = {Alexandr Kostochka and Jingwei Xu},
  journal= {arXiv preprint arXiv:2306.14295},
  year   = {2023}
}

Comments

19 pages, 1 figure. arXiv admin note: text overlap with arXiv:2006.10244

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