{"paper":{"title":"Finding Shortest Paths between Graph Colourings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Dani\\\"el Paulusma, Dieter Kratsch, Matthew Johnson, Stefan Kratsch, Viresh Patel","submitted_at":"2014-03-25T13:56:21Z","abstract_excerpt":"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-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6347","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}