{"paper":{"title":"Simple vertex coloring algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.DS","authors_text":"Fang Song, Jackson Morris","submitted_at":"2021-02-14T07:27:10Z","abstract_excerpt":"Given a graph $G$ with $n$ vertices and maximum degree $\\Delta$, it is known that $G$ admits a vertex coloring with $\\Delta + 1$ colors such that no edge of $G$ is monochromatic. This can be seen constructively by a simple greedy algorithm, which runs in time $O(n\\Delta)$.\n  Very recently, a sequence of results (e.g., [Assadi et. al. SODA'19, Bera et. al. ICALP'20, Alon Assadi Approx/Random'20]) show randomized algorithms for $(\\epsilon + 1)\\Delta$-coloring in the query model making $\\tilde{O}(n\\sqrt{n})$ queries, improving over the greedy strategy on dense graphs. In addition, a lower bound o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07089","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/2102.07089/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"}