{"paper":{"title":"On the choice number of complete multipartite graphs with part size four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Salmon, H. A. Kierstead, Ran Wang","submitted_at":"2014-07-14T21:09:19Z","abstract_excerpt":"Let $\\mathrm{ch}(G)$ denote the choice number of a graph $G$, and let $K_{s*k}$ be the complete $k$-partite graph with $s$ vertices in each part. Erd\\H{o}s, Rubin, and Taylor showed that $\\mathrm{ch}( K_{2*k})=k$, and suggested the problem of determining the choice number of $K_{s*k}.$ The first author established\n  $\\mathrm{ch}( K_{3*k})=\\left\\lceil \\frac{4k-1}{3}\\right\\rceil$. Here we prove $\\mathrm{ch} (K_{4*k})=\\left\\lceil \\frac{3k-1}{2}\\right\\rceil$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3817","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"}