%A Feghali, Carl
%A Fiala, Jiří
%D 2019
%T Reconfiguration graph for vertex colourings of weakly chordal graphs
%K
%X The reconfiguration graph $R_k(G)$ of the $k$-colourings of a graph $G$ contains as its vertex set the $k$-colourings of $G$ and two colourings are joined by an edge if they differ in colour on just one vertex of $G$. We show that for each $k \geq 3$ there is a $k$-colourable weakly chordal graph $G$ such that $R_{k+1}(G)$ is disconnected. We also introduce a subclass of $k$-colourable weakly chordal graphs which we call $k$-colourable compact graphs and show that for each $k$-colourable compact graph $G$ on $n$ vertices, $R_{k+1}(G)$ has diameter $O(n^2)$. We show that this class contains all $k$-colourable co-chordal graphs and when $k = 3$ all $3$-colourable $(P_5, \overline{P_5}, C_5)$-free graphs. We also mention some open problems.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1232
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 667-671%V 88
%N 3
%@ 0862-9544
%8 2019-07-30