List-coloring claw-free graphs with $\Delta$-1 colors

Daniel W. Cranston; Landon Rabern

List-coloring claw-free graphs with $\Delta$-1 colors

Combinatorics 2017-05-15 v1

Authors: Daniel W. Cranston , Landon Rabern

Abstract

We prove that if $G$ is a quasi-line graph with $\Delta(G)>\omega(G)$ and $\Delta(G)\ge 69$ , then $\chi_{OL}(G)\le \Delta(G)-1$ . Together with our previous work, this implies that if $G$ is a claw-free graph with $\Delta(G)>\omega(G)$ and $\Delta(G)\ge 69$ , then $\chi_{\ell}(G)\le \Delta(G)-1$ .

Keywords

list coloring claw-free graphs quasi-line graphs chromatic number graph theory maximum degree clique number

Cite

@article{arxiv.1508.03574,
  title  = {List-coloring claw-free graphs with $\Delta$-1 colors},
  author = {Daniel W. Cranston and Landon Rabern},
  journal= {arXiv preprint arXiv:1508.03574},
  year   = {2017}
}

Comments

24 pages, 5 figures

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