{"paper":{"title":"Constant-Time Dynamic $(\\Delta+1)$-Coloring and Weight Approximation for Minimum Spanning Forest: Dynamic Algorithms Meet Property Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Monika Henzinger, Pan Peng","submitted_at":"2019-07-10T14:21:06Z","abstract_excerpt":"With few exceptions (namely, algorithms for maximal matching, $2$-approximate vertex cover, and certain constant-stretch spanners), all known fully dynamic algorithms in general graphs require (amortized) $\\Omega(\\log n)$ update/query time. Showing for the first time that techniques from property testing can lead to constant-time fully dynamic graph algorithms we prove the following results:\n  (1) We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper $(\\Delta+1)$-vertex coloring of a graph with maximum degree at most $\\Delt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04745","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"}