# 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}
}
• Published in ESA 3 July 2019
• Mathematics, Computer Science
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
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