{"paper":{"title":"Spanning trees in sparse expanders","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donglei Yang, Jie Han","submitted_at":"2022-11-09T09:22:52Z","abstract_excerpt":"Given integers $n\\ge \\Delta\\ge 2$, let $\\mathcal{T}(n, \\Delta)$ be the collection of all $n$-vertex trees with maximum degree at most $\\Delta$. A question of Alon, Krivelevich and Sudakov in 2007 asks for determining the best possible spectral gap condition forcing an $(n, d,\\lambda)$-graph to be $\\mathcal{T}(n, \\Delta)$-universal, namely, it contains all members of $\\mathcal{T}(n, \\Delta)$ as a subgraph simultaneously. In this paper we show that for sufficiently large integer $n$ and all $\\Delta\\in \\mathbb{N}$, every $(n, d,\\lambda)$-graph with \\[ \\lambda\\le\\frac{d}{2\\Delta^{5\\sqrt{\\log n}}} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.04758","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/2211.04758/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"}