A counterexample to a conjecture of Bj\"{o}rner and Lov\'asz on the $\chi$-coloring complex

Shlomo Hoory; Nathan Linial

A counterexample to a conjecture of Bj\"{o}rner and Lov\'asz on the $\chi$-coloring complex

Combinatorics 2007-05-23 v2

Authors: Shlomo Hoory , Nathan Linial

Abstract

Associated with every graph $G$ of chromatic number $\chi$ is another graph $G'$ . The vertex set of $G'$ consists of all $\chi$ -colorings of $G$ , and two $\chi$ -colorings are adjacent when they differ on exactly one vertex. According to a conjecture of Bj\"{o}rner and Lov\'asz, this graph $G'$ must be disconnected. In this note we give a counterexample to this conjecture.

Keywords

graph coloring chromatic number conjecture counterexample chi-coloring complex disconnected graph

Cite

@article{arxiv.math/0405339,
  title  = {A counterexample to a conjecture of Bj\"{o}rner and Lov\'asz on the $\chi$-coloring complex},
  author = {Shlomo Hoory and Nathan Linial},
  journal= {arXiv preprint arXiv:math/0405339},
  year   = {2007}
}

Comments

To appear in JCTB

A counterexample to a conjecture of Bj\"{o}rner and Lov\'asz on the $\chi$-coloring complex

Abstract

Keywords

Cite

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