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

Shlomo Hoory*, Nathan Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 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 languageAmerican English
Pages (from-to)346-349
Number of pages4
JournalJournal of Combinatorial Theory. Series B
Volume95
Issue number2
DOIs
StatePublished - Nov 2005

Keywords

  • Coloring complex
  • Graph coloring
  • Graph homomorphism

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