{"paper":{"title":"Finding paths in sparse random graphs requires many queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Asaf Ferber, Benny Sudakov, Michael Krivelevich, Pedro Vieira","submitted_at":"2015-05-04T18:02:51Z","abstract_excerpt":"We discuss a new algorithmic type of problem in random graphs studying the minimum number of queries one has to ask about adjacency between pairs of vertices of a random graph $G\\sim {\\mathcal G}(n,p)$ in order to find a subgraph which possesses some target property with high probability. In this paper we focus on finding long paths in $G\\sim \\mathcal G(n,p)$ when $p=\\frac{1+\\varepsilon}{n}$ for some fixed constant $\\varepsilon>0$. This random graph is known to have typically linearly long paths.\n  To have $\\ell$ edges with high probability in $G\\sim \\mathcal G(n,p)$ one clearly needs to query"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00734","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"}