{"paper":{"title":"On the facial Thue choice number of plane graphs via entropy compression method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erika \\v{S}krabu\\v{l}\\'akov\\'a, Jakub Przyby{\\l}o, Jens Schreyer","submitted_at":"2013-08-23T14:06:30Z","abstract_excerpt":"Let $G$ be a plane graph. A vertex-colouring $\\varphi$ of $G$ is called {\\em facial non-repetitive} if for no sequence $r_1 r_2 \\dots r_{2n}$, $n\\geq 1$, of consecutive vertex colours of any facial path it holds $r_i=r_{n+i}$ for all $i=1,2,\\dots,n$. A plane graph $G$ is {\\em facial non-repetitively $l$-choosable} if for every list assignment $L:V\\rightarrow 2\\sp{\\mathbb{N}}$ with minimum list size at least $l$ there is a facial non-repetitive vertex-colouring $\\varphi$ with colours from the associated lists. The {\\em facial Thue choice number}, $\\pi_{fl}(G)$, of a plane graph $G$ is the minim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5128","kind":"arxiv","version":3},"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"}