{"paper":{"title":"On the subgraph query problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Moreira, Chady Ben Hamida, Ryan Alweiss, Xiaoyu He","submitted_at":"2019-11-11T17:39:56Z","abstract_excerpt":"Given a fixed graph $H$, a real number $p\\in(0,1)$, and an infinite Erd\\H{o}s-R\\'enyi graph $G\\sim G(\\infty,p)$, how many adjacency queries do we have to make to find a copy of $H$ inside $G$ with probability $1/2$? Determining this number $f(H,p)$ is a variant of the {\\it subgraph query problem} introduced by Ferber, Krivelevich, Sudakov, and Vieira. For every graph $H$, we improve the trivial upper bound of $f(H,p) = O(p^{-d})$, where $d$ is the degeneracy of $H$, by exhibiting an algorithm that finds a copy of $H$ in time $o(p^{-d})$ as $p$ goes to $0$. Furthermore, we prove that there are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.04413","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.04413/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"}