{"paper":{"title":"Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Abhishek Dhawan, Jonathan A. Noel, Peter Allen","submitted_at":"2026-07-28T21:02:45Z","abstract_excerpt":"Martinsson and Steiner recently proved that the fractional chromatic number of any $d$-degenerate triangle-free graph $G$ satisfies $\\chi_f(G) = O\\left(\\frac{d}{\\log d}\\right)$. They further conjectured a sharp leading constant $1 + o(1)$. In this paper, we confirm their upper bound conjecture for graphs having girth at least $5$. Our proof is constructive: it gives an efficient randomized algorithm that, with high probability, computes a fractional coloring of weight at most $(1 + o(1))\\frac{d}{\\log d}$ in such graphs.\n  Furthermore, we establish their conjectured lower bound in a stronger fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26271","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/2607.26271/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"}