Mixing 3-colourings in bipartite graphs

Cereceda, Luis; van den Heuvel, Jan; Johnson, Matthew

Abstract

For a 3-colourable graph G, the 3-colour graph of G, denoted C3(G), is the graph with node set the proper vertex 3-colourings of G, and two nodes adjacent whenever the corresponding colourings differ on precisely one vertex of G. We consider the following question : given G, how easily can we decide whether or not C3(G) is connected? We show that the 3-colour graph of a 3-chromatic graph is never connected, and characterise the bipartite graphs for which C3(G) is connected. We also show that the problem of deciding the connectedness of the 3-colour graph of a bipartite graph is coNP-complete, but that restricted to planar bipartite graphs, the question is answerable in polynomial time.

Citation

Cereceda, L., van den Heuvel, J., & Johnson, M. (online). Mixing 3-colourings in bipartite graphs. Lecture Notes in Computer Science, 166-177. https://doi.org/10.1007/978-3-540-74839-7_17

• Journal Article Type: Article
• Deposit Date: Oct 7, 2009
• Publicly Available Date: Oct 28, 2009
• Journal: Lecture Notes in Computer Science
• Print ISSN: 0302-9743
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Issue: 4769
• Pages: 166-177
• DOI: https://doi.org/10.1007/978-3-540-74839-7_17
• Public URL: https://durham-repository.worktribe.com/output/1547849