{"paper":{"title":"The list chromatic number of graphs with small clique number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Molloy","submitted_at":"2017-01-31T17:09:05Z","abstract_excerpt":"We prove that every triangle-free graph with maximum degree $\\Delta$ has list chromatic number at most $(1+o(1))\\frac{\\Delta}{\\ln \\Delta}$. This matches the best-known bound for graphs of girth at least 5. We also provide a new proof that for any $r\\geq 4$ every $K_r$-free graph has list-chromatic number at most $200r\\frac{\\Delta\\ln\\ln\\Delta}{\\ln\\Delta}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.09133","kind":"arxiv","version":2},"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"}