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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.26271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-28T21:02:45Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"2f70d37eca3d389d38a2282cb34b1da27b06091143f7a6fc1157906b1aade37d","abstract_canon_sha256":"a42d4f6836868c89d36c1c7a0c1adc3983af391fc9c846f87e88503ecae1be9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d8262959001aec738cd00cebb5b6daa5796b42e4f5be15467d26d9e130ec892","last_reissued_at":"2026-07-30T01:17:53.156973Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-30T01:17:53.156973Z"},"graph_snapshot":{"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. 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