{"paper":{"title":"The Complexity of Distributed Edge Coloring with Small Palettes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Jara Uitto, Qizheng He, Seth Pettie, Wenzheng Li, Yi-Jun Chang","submitted_at":"2017-08-14T19:47:53Z","abstract_excerpt":"The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes.\n  1. We simplify the \\emph{round elimination} technique of Brandt et al. and prove that $(2\\Delta-2)$-edge coloring requires $\\Omega(\\log_\\Delta \\log n)$ time w.h.p. and $\\Omega(\\log_\\Delta n)$ time deterministically, even on trees. The simplified technique is based on two ideas: the notion of an irregular running time and some general observations that transfo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04290","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":""},"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"}