# Recolouring planar graphs of girth at least five

@inproceedings{Bartier2021RecolouringPG, title={Recolouring planar graphs of girth at least five}, author={Valentin Bartier and Nicolas Bousquet and Carl Feghali and Marc Heinrich and Benjamin Moore and Th{\'e}o Pierron}, year={2021} }

For a positive integer k , the k -recolouring graph of a graph G has as vertex set all proper k -colourings of G with two k -colourings being adjacent if they diﬀer by the colour of exactly one vertex. A result of Dyer et al. regarding graphs of bounded degeneracy implies that the 7 -recolouring graphs of planar graphs, the 5 -recolouring graphs of triangle-free planar graphs and the 4 -recolouring graphs planar graphs of girth at least six are connected. On the other hand, there are planar…

## 6 Citations

### 5-Coloring Reconfiguration of Planar Graphs with No Short Odd Cycles

- Mathematics
- 2022

The coloring reconﬁguration graph C k ( G ) has as its vertex set all the proper k -colorings of G , and two vertices in C k ( G ) are adjacent if their corresponding k -colorings diﬀer on a single…

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

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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…

### Optimally Reconfiguring List and Correspondence Colourings

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The reconﬁguration graph C k ( G ) for the k -colourings of a graph G has a vertex for each proper k -colouring of G , and two vertices of C k ( G ) are adjacent precisely when those k -colourings…

### Short and local transformations between ($\Delta+1$)-colorings

- Mathematics
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Recoloring a graph is about finding a sequence of proper colorings of this graph from an initial coloring σ to a target coloring η. Each pair of consecutive colorings must differ on exactly one…

### Short and local transformations between (Δ+1)-colorings

- MathematicsArXiv
- 2022

Recoloring a graph is about (cid:28)nding a sequence of proper colorings of this graph from an initial coloring σ to a target coloring η . Each pair of consecutive colorings must di(cid:27)er on…

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