Sparse critical graphs for defective $(1,3)$-coloring

Alexandr Kostochka; Jingwei Xu; Xuding Zhu

Sparse critical graphs for defective $(1,3)$-coloring

Combinatorics 2023-10-13 v1

Authors: Alexandr Kostochka , Jingwei Xu , Xuding Zhu

Abstract

A graph $G$ is $(1,3)$ -colorable if its vertices can be partitioned into subsets $V_1$ and $V_2$ so that every vertex in $G[V_1]$ has degree at most $1$ and every vertex in $G[V_2]$ has degree at most $3$ . We prove that every graph with maximum average degree at most 28/9 is $(1, 3)$ -colorable.

Keywords

graph coloring rainbow coloring graph pebbling

Cite

@article{arxiv.2310.08486,
  title  = {Sparse critical graphs for defective $(1,3)$-coloring},
  author = {Alexandr Kostochka and Jingwei Xu and Xuding Zhu},
  journal= {arXiv preprint arXiv:2310.08486},
  year   = {2023}
}

Comments

21 pages

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