{"paper":{"title":"List Coloring a Cartesian Product with a Complete Bipartite Factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hemanshu Kaul, Jeffrey A. Mudrock","submitted_at":"2018-11-02T18:30:42Z","abstract_excerpt":"We study the list chromatic number of the Cartesian product of any graph $G$ and a complete bipartite graph with partite sets of size $a$ and $b$, denoted $\\chi_\\ell(G \\square K_{a,b})$. We have two motivations. A classic result on the gap between list chromatic number and the chromatic number tells us $\\chi_\\ell(K_{a,b}) = 1 + a$ if and only if $b \\geq a^a$. Since $\\chi_\\ell(K_{a,b}) \\leq 1 + a$ for any $b \\in \\mathbb{N}$, this result tells us the values of $b$ for which $\\chi_\\ell(K_{a,b})$ is as large as possible and far from $\\chi(K_{a,b})=2$. In this paper we seek to understand when $\\chi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02420","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"}