Building a larger class of graphs for efficient reconfiguration of vertex colouring

@article{Biedl2020BuildingAL,
  title={Building a larger class of graphs for efficient reconfiguration of vertex colouring},
  author={Therese C. Biedl and Anna Lubiw and Owen D. Merkel},
  journal={ArXiv},
  year={2020},
  volume={abs/2003.01818}
}
A $k$-colouring of a graph $G$ is an assignment of at most $k$ colours to the vertices of $G$ so that adjacent vertices are assigned different colours. The reconfiguration graph of the $k$-colourings, $\mathcal{R}_k(G)$, is the graph whose vertices are the $k$-colourings of $G$ and two colourings are joined by an edge in $\mathcal{R}_k(G)$ if they differ in colour on exactly one vertex. For a $k$-colourable graph $G$, we investigate the connectivity and diameter of $\mathcal{R}_{k+1}(G)$. It is… 
C O ] 2 A ug 2 02 1 Mixing colourings in 2 K 2-free graphs
The reconfiguration graph for the k-colourings of a graph G, denoted Rk(G), is the graph whose vertices are the k-colourings of G and two colourings are joined by an edge if they differ in colour on
Recolouring weakly chordal graphs and the complement of triangle-free graphs
TLDR
It is proved that for all n ≥ 1, there exists a k-colourable weakly chordal graph G where Rk+n(G) is disconnected, answering an open question of Feghali and Fiala.

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