{"paper":{"title":"List $k$-Colouring $P_t$-Free Graphs: a Mim-width Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Andrea Munaro, Daniel Paulusma, Jake Horsfield, Nick Brettell","submitted_at":"2020-08-03T14:58:57Z","abstract_excerpt":"A colouring of a graph $G=(V,E)$ is a mapping $c\\colon V\\to \\{1,2,\\ldots\\}$ such that $c(u)\\neq c(v)$ for every two adjacent vertices $u$ and $v$ of $G$. The {\\sc List $k$-Colouring} problem is to decide whether a graph $G=(V,E)$ with a list $L(u)\\subseteq \\{1,\\ldots,k\\}$ for each $u\\in V$ has a colouring $c$ such that $c(u)\\in L(u)$ for every $u\\in V$. Let $P_t$ be the path on $t$ vertices and let $K_{1,s}^1$ be the graph obtained from the $(s+1)$-vertex star $K_{1,s}$ by subdividing each of its edges exactly once.Recently, Chudnovsky, Spirkl and Zhong (DM 2020) proved that List $3$-Colouring"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01590","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.01590/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}