{"paper":{"title":"Bounding the weight choosability number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Seamone","submitted_at":"2012-10-25T18:50:04Z","abstract_excerpt":"Let $G = (V,E)$ be a graph, and for each $e \\in E(G)$, let $L_e$ be a list of real numbers. Let $w:E(G) \\to \\cup_{e \\in E(G)}L_e$ be an edge weighting function such that $w(e) \\in L_e$ for each $e \\in E(G)$, and let $c_w$ be the vertex colouring obtained by $c_w(v) = \\sum_{e \\ni v}w(e)$. We desire the smallest possible $k$ such that, for any choice of $\\{L_e \\,|\\, e \\in E(G)\\}$ where $|L_e| \\geq k$ for all $e \\in E(G)$, there exists an edge weighting function $w$ for which $c_w$ is proper. The smallest such value of $k$ is the weight choosability number of $G$.\n  This colouring problem, introd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6944","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"}