{"paper":{"title":"List colorings of $K_5$-minor-free graphs with special list assignments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anja Pruchnewski, Daniel W. Cranston, Margit Voigt, Zsolt Tuza","submitted_at":"2011-05-12T17:14:57Z","abstract_excerpt":"A {\\it list assignment} $L$ of a graph $G$ is a function that assigns a set (list) $L(v)$ of colors to every vertex $v$ of $G$. Graph $G$ is called {\\it $L$-list colorable} if it admits a vertex coloring $\\phi$ such that $\\phi(v)\\in L(v)$ for all $v\\in V(G)$ and $\\phi(v)\\not=\\phi(w)$ for all $vw\\in E(G)$.\n  The following question was raised by Bruce Richter. Let $G$ be a planar, 3-connected graph that is not a complete graph. Denoting by $d(v)$ the degree of vertex $v$, is $G$ $L$-list colorable for every list assignment $L$ with $|L(v)|=\\min \\{d(v), 6\\}$ for all $v\\in V(G)$?\n  More generally,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2532","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"}