{"paper":{"title":"Sandwiching random regular graphs between binomial random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendan McKay, Mikhail Isaev, Pu Gao","submitted_at":"2019-06-07T03:36:13Z","abstract_excerpt":"Kim and Vu made the following conjecture (\\textit{Advances in Mathematics}, 2004): if $d\\gg \\log n$, then the random $d$-regular graph $\\mathcal G(n,d)$ can asymptotically almost surely be \"sandwiched\" between $\\mathcal G(n,p_1)$ and $\\mathcal G(n,p_2)$ where $p_1$ and $p_2$ are both $(1+o(1))d/n$. They proved this conjecture for $\\log n\\ll d\\le n^{1/3-o(1)}$, with a defect in the sandwiching: $\\mathcal G(n,d)$ contains $\\mathcal G(n,p_1)$ perfectly, but is not completely contained in $\\mathcal G(n,p_2)$. Recently, the embedding $\\mathcal G(n,p_1) \\subseteq \\mathcal G(n,d)$ was improved by Dud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02886","kind":"arxiv","version":5},"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/1906.02886/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"}