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A conjecture of Cereceda from 2007 asserts that for every integer $\\ell \\geq k + 2$ and $k$-degenerate graph $G$ on $n$ vertices, $R_{\\ell}(G)$ has diameter $O(n^2)$. The conjecture has been verified only when $\\ell \\geq 2k + 1$. We give a simple proof that if $G$ is a planar graph on $n$ vertices, then $R_{10}(G)$ has diameter at most $n^2$. 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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 exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer $\\ell \\geq k + 2$ and $k$-degenerate graph $G$ on $n$ vertices, $R_{\\ell}(G)$ has diameter $O(n^2)$. The conjecture has been verified only when $\\ell \\geq 2k + 1$. We give a simple proof that if $G$ is a planar graph on $n$ vertices, then $R_{10}(G)$ has diameter at most $n^2$. 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