{"paper":{"title":"On Edge Coloring of Multigraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guangming Jing","submitted_at":"2023-08-29T19:32:21Z","abstract_excerpt":"Let $\\Delta(G)$ and $\\chi'(G)$ be the maximum degree and chromatic index of a graph $G$, respectively. Appearing in different forms, Gupta\\,(1967), Goldberg\\,(1973), Andersen\\,(1977), and Seymour\\,(1979) made the following conjecture: Every multigraph $G$ satisfies $\\chi'(G) \\le \\max\\{ \\Delta(G) + 1, \\Gamma(G) \\}$, where $\\Gamma(G) = \\max_{H \\subseteq G, |V(H)|\\geq 2} \\left\\lceil \\frac{ |E(H)| }{ \\lfloor \\tfrac{1}{2} |V(H)| \\rfloor} \\right\\rceil$ is the density of $G$. In this paper, we present a polynomial-time algorithm for coloring any multigraph with $\\max\\{ \\Delta(G) + 1, \\Gamma(G) \\}$ co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.15588","kind":"arxiv","version":6},"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/2308.15588/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"}