# Linear transformations between colorings in chordal graphs

@inproceedings{Bousquet2019LinearTB, title={Linear transformations between colorings in chordal graphs}, author={Nicolas Bousquet and Valentin Bartier}, booktitle={ESA}, year={2019} }

Let $k$ and $d$ be such that $k \ge d+2$. Consider two $k$-colorings of a $d$-degenerate graph $G$. Can we transform one into the other by recoloring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that question in the affirmative, and exhibited a recolouring sequence of exponential length.
If $k=d+2$, we know that there exists graphs for which a quadratic number of recolorings is needed. And when $k=2d+2$, there always exists a linear… Expand

#### 4 Citations

An Update on Reconfiguring $10$-Colorings of Planar Graphs

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- Electron. J. Comb.
- 2020

The number of colors is improved, showing that $R_{10}(G)$ has diameter at most $8n$ for every planar graph $G$ with $n$ vertices. Expand

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

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- ArXiv
- 2020

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. Expand

Recoloring graphs of treewidth 2

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- Discret. Math.
- 2021

It is proved that there always exists a linear transformation between any pair of 5colorings and this result is tight since there exist graphs of treewidth 2 and two 4-colorings such that a shortest transformation between them is quadratic. Expand

Distributed recoloring of interval and chordal graphs

- Computer Science
- ArXiv
- 2021

It is proved that, if the authors have less than 2ω colors, ω being the size of the largest clique, extra colors will be needed in the intermediate colorings of interval and chordal graphs, which improves on previous known algorithms that use ω + 2 colors for the same running times. Expand

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