{"paper":{"title":"Triangle-free $d$-degenerate graphs have small fractional chromatic number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Anders Martinsson","submitted_at":"2025-01-30T09:54:39Z","abstract_excerpt":"A well-known conjecture by Harris states that any triangle-free $d$-degenerate graph has fractional chromatic number at most $O\\left(\\frac{d}{\\ln d}\\right)$. This conjecture has gained much attention in recent years, and is known to have many interesting implications, including a conjecture by Esperet, Kang and Thomass\\'e that any triangle-free graph with minimum degree $d$ contains a bipartite induced subgraph of minimum degree $\\Omega(\\log d)$. Despite this attention, Harris' conjecture has remained wide open with no known improvement on the trivial upper bound, until now.\n  In this article,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18238","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/2501.18238/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"}