{"paper":{"title":"Spanning trees in pseudorandom graphs via sorting networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alp M\\\"uyesser, Joseph Hyde, Mat\\'ias Pavez-Sign\\'e, Natasha Morrison","submitted_at":"2023-11-06T15:25:13Z","abstract_excerpt":"We show that $(n,d,\\lambda)$-graphs with $\\lambda=O(d/\\log^3 n)$ are universal with respect to all bounded degree spanning trees. This significantly improves upon the previous best bound due to Han and Yang of the form $\\lambda=d/\\exp{(O(\\sqrt{\\log n}))}$, and makes progress towards a problem of Alon, Krivelevich, and Sudakov from 2007. Our proof relies on the existence of sorting networks of logarithmic depth, as given by a celebrated construction of Ajtai, Koml\\'os and Szemer\\'edi. Using this construction, we show that the classical vertex-disjoint paths problem can be solved for a set of ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03185","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/2311.03185/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"}