A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
Computational complexity of compaction to irreflexive cycles
Journal of Computer and System Sciences
Random sampling of 3-colorings in ℤ2
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Finding Paths between graph colourings: PSPACE-completeness and superpolynomial distances
Theoretical Computer Science
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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.