{"paper":{"title":"Finding Planted Cycles in a Random Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Colin Sandon, Dana Yang, Jiaming Xu, Julia Gaudio","submitted_at":"2025-11-06T04:57:48Z","abstract_excerpt":"In this paper, we study the problem of finding a collection of planted cycles in an \\ER random graph $G \\sim \\mathcal{G}(n, \\lambda/n)$, in analogy to the famous Planted Clique Problem. When the cycles are planted on a uniformly random subset of $\\delta n$ vertices, we show that almost-exact recovery (that is, recovering all but a vanishing fraction of planted-cycle edges as $n \\to \\infty$) is information-theoretically possible if $\\lambda < \\frac{1}{(\\sqrt{2 \\delta} + \\sqrt{1-\\delta})^2}$ and impossible if $\\lambda > \\frac{1}{(\\sqrt{2 \\delta} + \\sqrt{1-\\delta})^2}$. Moreover, despite the wors"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.04058","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/2511.04058/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"}