Publication details for Professor Matthew JohnsonBonsma, Paul Cereceda, Luis van den Heuvel, Jan & Johnson, Matthew (2007). Finding Paths between Graph Colourings: Computational Complexity and Possible Distances. Electronic Notes in Discrete Mathematics 29: 463-469.
- Publication type: Journal Article
- ISSN/ISBN: 1571-0653 (print)
- DOI: 10.1016/j.endm.2007.07.073
- Keywords: Colour graph, PSPACE-completeness, Superpolynomial paths.
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
Suppose we are given a graph G together with two proper vertex k-colourings of G, α and β. How easily can we decide whether it is possible to transform α into β by recolouring vertices of G one at a time, making sure we always have a proper k-colouring of G?
We prove a dichotomy theorem for the computational complexity of this decision problem: for values of k⩽3 the problem is polynomial-time solvable, while for any fixed k⩾4 it is PSPACE-complete. What is more, we establish a connection between the complexity of the problem and its underlying structure: we prove that for k⩽3 the minimum number of necessary recolourings is polynomial in the size of the graph, while for k⩾4 instances exist where this number is superpolynomial.