{"paper":{"title":"New bounds on the classical and quantum communication complexity of some graph properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Gabor Ivanyos, Hartmut Klauck, Miklos Santha, Ronald de Wolf, Troy Lee","submitted_at":"2012-04-20T12:14:18Z","abstract_excerpt":"We study the communication complexity of a number of graph properties where the edges of the graph $G$ are distributed between Alice and Bob (i.e., each receives some of the edges as input). Our main results are:\n  * An Omega(n) lower bound on the quantum communication complexity of deciding whether an n-vertex graph G is connected, nearly matching the trivial classical upper bound of O(n log n) bits of communication.\n  * A deterministic upper bound of O(n^{3/2}log n) bits for deciding if a bipartite graph contains a perfect matching, and a quantum lower bound of Omega(n) for this problem.\n  *"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4596","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"}