## 5 Citations

### C O ] 2 A ug 2 02 1 Mixing colourings in 2 K 2-free graphs

- Mathematics
- 2021

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…

### Towards a conjecture on the recoloring diameter of planar graphs

- MathematicsArXiv
- 2022

A list assignment L of a graph G is a function that assigns to every vertex v of G a set L ( v ) of colors. A proper coloring α of G is called an L -coloring of G if α ( v ) ∈ L ( v ) for every v ∈ V…

### List recoloring of planar graphs

- Mathematics
- 2022

A list assignment L of a graph G is a function that assigns to every vertex v of G a set L ( v ) of colors. A proper coloring α of G is called an L -coloring of G if α ( v ) ∈ L ( v ) for every v ∈ V…

### Reconfiguration of vertex colouring and forbidden induced subgraphs

- Mathematics
- 2022

The reconfiguration graph of the $k$-colourings, denoted $\mathcal{R}_k(G)$, is the graph whose vertices are the $k$-colourings of $G$ and two colourings are adjacent in $\mathcal{R}_k(G)$ if they…

## 7 References

### Reconfiguration graphs for vertex colourings of chordal and chordal bipartite graphs

- MathematicsJ. Comb. Optim.
- 2014

It is proved that for each k≥2 there is a k-colourable chordal graph G whose reconfiguration graph of the (k+1)-colourings has diameter Θ(|V|2).

### Reconfiguration Graph for Vertex Colourings of Weakly Chordal Graphs

- MathematicsDiscret. Math.
- 2020

### The Strong Perfect Graph Theorem

- Mathematics
- 2002

A graph G is perfect if for every induced subgraph H, the chromatic number of H equals the size of the largest complete subgraph of H, and G is Berge if no induced subgraph of G is an odd cycle of…

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

- MathematicsTrends in Mathematics
- 2021

It is proved that if G is a $k-colourable OAT graph then $\mathcal{R}_{k+1}(G)$ is connected with diameter $O(n^2)$ and polynomial time algorithms to recognize OAT graphs are given.