{"paper":{"title":"Faster Dynamic $(\\Delta+1)$-Coloring Against Adaptive Adversaries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Magn\\'us M. Halld\\'orsson, Maxime Flin","submitted_at":"2025-04-28T12:28:45Z","abstract_excerpt":"We consider the problem of maintaining a proper $(\\Delta + 1)$-vertex coloring in a graph on $n$-vertices and maximum degree $\\Delta$ undergoing edge insertions and deletions. We give a randomized algorithm with amortized update time $\\widetilde{O}( n^{2/3} )$ against adaptive adversaries, meaning that updates may depend on past decisions by the algorithm. This improves on the very recent $\\widetilde{O}( n^{8/9} )$-update-time algorithm by Behnezhad, Rajaraman, and Wasim (SODA 2025) and matches a natural barrier for dynamic $(\\Delta+1)$-coloring algorithms. The main improvements are in the den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.19729","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.19729/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"}