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- W2894077664 abstract "The reconfiguration graph $R_k(G)$ of the $k$-colourings of a graph $G$ has as vertex set the set of all possible $k$-colourings of $G$ and two colourings are adjacent if they differ on the colour of exactly one vertex. Cereceda conjectured ten years ago that, for every $k$-degenerate graph $G$ on $n$ vertices, $R_{k+2}(G)$ has diameter $mathcal{O}({n^2})$. The conjecture is wide open, with a best known bound of $mathcal{O}({k^n})$, even for planar graphs. We improve this bound for planar graphs to $2^{mathcal{O}({sqrt{n}})}$. Our proof can be transformed into an algorithm that runs in $2^{mathcal{O}({sqrt{n}})}$ time." @default.
- W2894077664 created "2018-10-05" @default.
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- W2894077664 date "2018-10-01" @default.
- W2894077664 modified "2023-09-27" @default.
- W2894077664 title "Towards Cereceda's conjecture for planar graphs" @default.
- W2894077664 hasPublicationYear "2018" @default.
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