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

Shlomo Hoory; Nathan Linial

doi:10.1016/j.jctb.2005.06.008

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

Shlomo Hoory^*, Nathan Linial

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	346-349
Number of pages	4
Journal	Journal of Combinatorial Theory. Series B
Volume	95
Issue number	2
DOIs	https://doi.org/10.1016/j.jctb.2005.06.008
State	Published - Nov 2005

Keywords

Coloring complex
Graph coloring
Graph homomorphism

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10.1016/j.jctb.2005.06.008

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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 Bj{\"o}rner and Lov{\'a}sz, this graph G′ must be disconnected. In this note we give a counterexample to this conjecture.",

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KW - Graph coloring

KW - Graph homomorphism

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

Abstract

Keywords

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