Mixing 3-colourings in bipartite graphs

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

doi:10.1016/j.ejc.2009.03.011

Mixing 3-colourings in bipartite graphs

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

Authors

Luis Cereceda

Jan van den Heuvel

Professor Matthew Johnson matthew.johnson2@durham.ac.uk
Head Of Department

Abstract

For a 3-colourable graph G, the 3-colour graph of G, denoted C_3(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 one decide whether or not C_3(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 View the MathML source 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. (2009). Mixing 3-colourings in bipartite graphs. European Journal of Combinatorics, 30(7), 1593-1606. https://doi.org/10.1016/j.ejc.2009.03.011

Journal Article Type	Article
Publication Date	Oct 1, 2009
Deposit Date	Sep 30, 2010
Publicly Available Date	Oct 29, 2010
Journal	European Journal of Combinatorics
Print ISSN	0195-6698
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	30
Issue	7
Pages	1593-1606
DOI	https://doi.org/10.1016/j.ejc.2009.03.011