A counterexample to a conjecture of Björner and Lovász on the $χ$-coloring complex

Details A counterexample to a conjecture of Björner and Lovász on the $χ$-coloring complex A counterexample to a conjecture of Björner and Lovász on the $χ$-coloring complex

2004-05-17

arxiv.org/abs/math/0405339v2

Mathematics

Combinatorics

To appear in JCTB

Scientific paper

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.

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