{"paper":{"title":"Spanning clique subdivisions in pseudorandom graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hyunwoo Lee, Mat\\'ias Pavez-Sign\\'e, Teo Petrov","submitted_at":"2025-04-02T11:46:24Z","abstract_excerpt":"In this paper, we study the appearance of a spanning subdivision of a clique in graphs satisfying certain pseudorandom conditions. Specifically, we show the following three results. Firstly, that there are constants $C>0$ and $c\\in (0,1]$ such that, whenever $d/\\lambda\\ge C$, every $(n,d,\\lambda)$-graph contains a spanning subdivision of $K_t$ for all $2\\le t \\le \\min\\{cd,c\\sqrt{\\frac{n}{\\log n}}\\}$. Secondly, that there are constants $C>0$ and $c\\in (0,1]$ such that, whenever $d/\\lambda\\ge C\\log^3n$, every $(n,d,\\lambda)$-graph contains a spanning nearly-balanced subdivision of $K_t$ for all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.01642","kind":"arxiv","version":1},"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/2504.01642/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"}