@article { ,
title = {Finding Paths between Graph Colourings: Computational Complexity and Possible Distances},
abstract = {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.},
doi = {10.1016/j.endm.2007.07.073},
issn = {1571-0653},
journal = {Electronic Notes in Discrete Mathematics},
note = {EPrint Processing Status: Author unable to supply full text},
pages = {463-469},
publicationstatus = {Published},
publisher = {Elsevier},
volume = {29},
keyword = {Algorithms and Complexity in Durham (ACiD), Colour graph, PSPACE-completeness, Superpolynomial paths.},
year = {2007},
author = {Bonsma, Paul and Cereceda, Luis and van den Heuvel, Jan and Johnson, Matthew}
}