A counterexample to a conjecture of Björner and Lovász on the χ-coloring complex
Shlomo Hoory, Nathan Linial
Abstract
Associated with every graph G of chromatic number χ is another graph G'. The vertex set of G' consists of all χ-colorings of G, and two χ-colorings are adjacent when they differ on exactly one vertex. According to a conjecture of Björner and Lovász, this graph G' must be disconnected. In this note we give a counterexample to this conjecture.
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