{"paper":{"title":"Bipartite graphs are $(\\frac{4}{5}-\\varepsilon) \\frac{\\Delta}{\\log \\Delta}$-choosable","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bojan Mohar, Ladislav Stacho, Peter Bradshaw","submitted_at":"2024-09-03T00:56:37Z","abstract_excerpt":"Alon and Krivelevich conjectured that if $G$ is a bipartite graph of maximum degree $\\Delta$, then the choosability (or list chromatic number) of $G$ satisfies $\\chi_{\\ell}(G) = O \\left ( \\log \\Delta \\right )$. Currently, the best known upper bound for $\\chi_{\\ell}(G)$ is $(1 + o(1)) \\frac{\\Delta}{\\log \\Delta}$, which also holds for the much larger class of triangle-free graphs. We prove that for $\\varepsilon = 10^{-3}$, every bipartite graph $G$ of sufficiently large maximum degree $\\Delta$ satisfies $\\chi_{\\ell}(G) < (\\frac{4}{5} -\\varepsilon) \\frac{\\Delta}{\\log \\Delta}$. This improved upper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01513","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.01513/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}