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.