Cereceda, Luis, van den Heuvel, Jan and Johnson, Matthew (2009) Mixing 3-colourings in bipartite graphs. European journal of combinatorics, 30 (7). pp. 1593-1606. ISSN 0195-6698
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 one 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.
|Additional Information:||© 2009 Elsevier Ltd.|
|Library of Congress subject classification:||Q Science > QA Mathematics
H Social Sciences > HA Statistics
|Sets:||Departments > Mathematics|
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