{"paper":{"title":"Chromatic index determined by fractional chromatic index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guantao Chen, Luke Postle, Ringi Kim, Songling Shan, Yuping Gao","submitted_at":"2016-06-25T16:09:15Z","abstract_excerpt":"Given a graph $G$ possibly with multiple edges but no loops, denote by $\\Delta$ the {\\it maximum degree}, $\\mu$ the {\\it multiplicity}, $\\chi'$ the {\\it chromatic index} and $\\chi_f'$ the {\\it fractional chromatic index} of $G$, respectively. It is known that $\\Delta\\le \\chi_f' \\le \\chi' \\le \\Delta + \\mu$, where the upper bound is a classic result of Vizing. While deciding the exact value of $\\chi'$ is a classic NP-complete problem, the computing of $\\chi_f'$ is in polynomial time. In fact, it is shown that if $\\chi_f' > \\Delta$ then $\\chi_f'= \\max \\frac{|E(H)|}{\\lfloor |V(H)|/2\\rfloor}$, wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07927","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"}