{"paper":{"title":"Phase Transitions in Planted k-Factor Recovery","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Colin Sandon, Dana Yang, Jiaming Xu, Julia Gaudio","submitted_at":"2025-03-12T01:31:27Z","abstract_excerpt":"This paper studies the problem of inferring a $k$-factor, specifically a spanning $k$-regular graph, planted within an Erdos-Renyi random graph $G(n,\\lambda/n)$. We show that as the average degree $\\lambda$ surpasses the critical threshold of $1/k$, the inference problem undergoes a transition from almost exact recovery to partial recovery. Moreover, as $\\lambda$ tends to infinity, the accuracy of recovery diminishes to zero. In addition, we characterize the recovery accuracy of a linear-time iterative pruning algorithm and show that it achieves almost exact recovery when $\\lambda < 1/k$. A ke"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.08984","kind":"arxiv","version":3},"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/2503.08984/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"}