{"paper":{"title":"Deterministic Distributed Edge-Coloring via Hypergraph Maximal Matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fabian Kuhn, Manuela Fischer, Mohsen Ghaffari","submitted_at":"2017-04-10T09:03:11Z","abstract_excerpt":"We present a deterministic distributed algorithm that computes a $(2\\Delta-1)$-edge-coloring, or even list-edge-coloring, in any $n$-node graph with maximum degree $\\Delta$, in $O(\\log^7 \\Delta \\log n)$ rounds. This answers one of the long-standing open questions of \\emph{distributed graph algorithms} from the late 1980s, which asked for a polylogarithmic-time algorithm. See, e.g., Open Problem 4 in the Distributed Graph Coloring book of Barenboim and Elkin. The previous best round complexities were $2^{O(\\sqrt{\\log n})}$ by Panconesi and Srinivasan [STOC'92] and $\\tilde{O}(\\sqrt{\\Delta}) + O("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02767","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":""},"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"}