Coloration of $K_7^-$-minor free graphs

Boris Albar

Coloration of $K_7^-$-minor free graphs

Combinatorics 2014-02-13 v1

Authors: Boris Albar

Abstract

Hadwiger's conjecture says that every $K_t$ -minor free graph is $(t - 1)$ -colorable. This problem has been proved for $t \leq 6$ but remains open for $t \geq 7$ . $K_7$ -minor free graphs have been proved to be $8$ -colorable (Albar & Gon\c{c}alves, 2013). We prove here that $K_7^-$ -minor free graphs are $7$ -colorable, where $K_7^-$ is the graph obtained from $K_7$ by removing one edge.

Keywords

Hadwiger's conjecture graph coloring $K_7^-$-minor free graphs chromatic number

Cite

@article{arxiv.1402.2806,
  title  = {Coloration of $K_7^-$-minor free graphs},
  author = {Boris Albar},
  journal= {arXiv preprint arXiv:1402.2806},
  year   = {2014}
}

Comments

11 pages, 1 figure

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