On the diameter of reconfiguration graphs for vertex colourings

Bonamy, M.; Johnson, M.; Lignos, I.M.; Patel, V.; Paulusma, D.

Abstract

The reconfiguration graph of the k-colourings of a graph G contains as its vertex set the proper vertex k-colourings of G, and two colourings are joined by an edge in the reconfiguration graph if they differ in colour on just one vertex of G. We prove that for a graph G on n vertices that is chordal or chordal bipartite, if G is k-colourable, then the reconfiguration graph of its ℓ-colourings, for ℓ⩾k+1, is connected and has diameter O(n2). We show that this bound is asymptotically tight up to a constant factor.

Citation

Bonamy, M., Johnson, M., Lignos, I., Patel, V., & Paulusma, D. On the diameter of reconfiguration graphs for vertex colourings

• Presentation Conference Type: Conference Paper (published)
• Publication Date: Dec 1, 2011
• Deposit Date: Dec 6, 2011
• Publicly Available Date: Jan 9, 2015
• Journal: Electronic Notes in Discrete Mathematics
• Print ISSN: 1571-0653
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 38
• Issue: 1
• Pages: 161-166
• DOI: https://doi.org/10.1016/j.endm.2011.09.028
• Keywords: Reconfiguration, Graph colouring, Graph diameter.
• Public URL: https://durham-repository.worktribe.com/output/1157671