{"paper":{"title":"Streaming Edge Coloring with Asymptotically Optimal Colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mohammad Saneian, Soheil Behnezhad","submitted_at":"2023-05-02T18:27:26Z","abstract_excerpt":"Given a graph $G$, an edge-coloring is an assignment of colors to edges of $G$ such that any two edges sharing an endpoint receive different colors. By Vizing's celebrated theorem, any graph of maximum degree $\\Delta$ needs at least $\\Delta$ and at most $(\\Delta + 1)$ colors to be properly edge colored. In this paper, we study edge colorings in the streaming setting. The edges arrive one by one in an arbitrary order. The algorithm takes a single pass over the input and must output a solution using a much smaller space than the input size. Since the output of edge coloring is as large as its in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.01714","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/2305.01714/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"}