{"paper":{"title":"List-coloring graphs on surfaces with varying list-sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice M. Dean, Joan P. Hutchinson","submitted_at":"2012-06-18T14:22:08Z","abstract_excerpt":"Let $G$ be a graph embedded on a surface $S_\\varepsilon$ with Euler genus $\\varepsilon > 0$, and let $P\\subseteq V(G)$ be a set of vertices mutually at distance at least 4 apart. Suppose all vertices of $G$ have $H(\\varepsilon)$-lists and the vertices of $P$ are precolored, where $H(\\varepsilon)=\\Big\\lfloor\\frac{7 + \\sqrt{24\\varepsilon + 1}}{2}\\Big\\rfloor$ is the Heawood number. We show that the coloring of $P$ extends to a list-coloring of $G$ and that the distance bound of 4 is best possible. Our result provides an answer to an analogous question of Albertson about extending a precoloring of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3945","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"}