{"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. Let $f_H(G) = 1$ iff the input graph $G$ on $n$ vertices contains $H$ as a (not necessarily induced) subgraph. Let $\\alpha_H$ denote the cardinality of a maximum independent set of $H$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06361","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"}