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Brewster","submitted_at":"2017-12-01T05:45:40Z","abstract_excerpt":"For a fixed graph $H$, the reconfiguration problem for $H$-colourings (i.e. homomorphisms to $H$) asks: given a graph $G$ and two $H$-colourings $\\varphi$ and $\\psi$ of $G$, does there exist a sequence $f_0,\\dots,f_m$ of $H$-colourings such that $f_0=\\varphi$, $f_m=\\psi$ and $f_i(u)f_{i+1}(v)\\in E(H)$ for every $0\\leq i<m$ and $uv\\in E(G)$? If the graph $G$ is loop-free, then this is the equivalent to asking whether it possible to transform $\\varphi$ into $\\psi$ by changing the colour of one vertex at a time such that all intermediate mappings are $H$-colourings. 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