{"paper":{"title":"Graph Homomorphism Reconfiguration and Frozen $H$-Colourings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Benjamin Moore, Jae-Baek Lee, Jonathan A. Noel, Mark Siggers, Richard C. 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. In the affirmative, we say tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00200","kind":"arxiv","version":1},"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"}