On the diameter of reconfiguration graphs for vertex colourings
Résumé
The reconfiguration graph of the k-colourings of a graph G contains as its vertex set the proper vertex k-colourings of G, and two colourings are joined by an edge in the reconfiguration graph if they differ in colour on just one vertex of G. We prove that for a graph G on n vertices that is chordal or chordal bipartite, if G is k-colourable, then the reconfiguration graph of its l-colourings, for l>=k+1, is connected and has diameter O(n^2). We show that this bound is asymptotically tight up to a constant factor.
Domaines
Mathématique discrète [cs.DM]| Origine | Fichiers produits par l'(les) auteur(s) |
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