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In this paper we show:\n  \\[Q(f_H) = \\Omega\\left(\\sqrt{\\alpha_H \\cdot n}\\right),\\] where $Q(f_H)$ denotes the quantum query complexity of $f_H$.\n  As a consequence we obtain a lower bounds for $Q(f_H)$ in terms of several other parameters of $H$ such as the average degree, minimum vertex cover, chromatic number, and the critical probability.\n  We also use the above bound"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.06361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-09-21T19:54:51Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"aa51627543f11d2f2b5579406add8db871b84dee57c61f8744e31eff2fc19815","abstract_canon_sha256":"08701c8029c79d366dde58a4e7d6597fd1e573182d35eb04b9278677c9dc406b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:20.488649Z","signature_b64":"ZpZChm9b3wde1wqY4hb70XBe0Ik5/2GrcM50iOl1FZWPpMD8Yr7N+i3hnjZ2xoUT+NhWvXMCtDsfDzpqMeVpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5bd9a97e96b3d0c1ae5921f4949c1392a11ec6ac7b617274a4ec987ac98a200","last_reissued_at":"2026-05-18T01:32:20.487785Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:20.487785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Query Complexity of Subgraph Isomorphism and Homomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CC","authors_text":"Raghav Kulkarni, Supartha Podder","submitted_at":"2015-09-21T19:54:51Z","abstract_excerpt":"Let $H$ be a fixed graph on $n$ vertices. 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