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- W2953047303 abstract "The $k$-colouring reconfiguration problem asks whether, for a given graph $G$, two proper $k$-colourings $alpha$ and $beta$ of $G$, and a positive integer $ell$, there exists a sequence of at most $ell+1$ proper $k$-colourings of $G$ which starts with $alpha$ and ends with $beta$ and where successive colourings in the sequence differ on exactly one vertex of $G$. We give a complete picture of the parameterized complexity of the $k$-colouring reconfiguration problem for each fixed $k$ when parameterized by $ell$. First we show that the $k$-colouring reconfiguration problem is polynomial-time solvable for $k=3$, settling an open problem of Cereceda, van den Heuvel and Johnson. Then, for all $k geq 4$, we show that the $k$-colouring reconfiguration problem, when parameterized by $ell$, is fixed-parameter tractable (addressing a question of Mouawad, Nishimura, Raman, Simjour and Suzuki) but that it has no polynomial kernel unless the polynomial hierarchy collapses." @default.
- W2953047303 created "2019-06-27" @default.
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- W2953047303 date "2014-03-25" @default.
- W2953047303 modified "2023-10-03" @default.
- W2953047303 title "Finding Shortest Paths between Graph Colourings" @default.
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