{"paper":{"title":"Kim--Vu's sandwich conjecture is true for $d \\gg \\log^4 n$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendan McKay, Mikhail Isaev, Pu Gao","submitted_at":"2020-11-18T18:26:00Z","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 $G(n,d)$ can be ``sandwiched'' between $G(n,p_*)$ and $G(n,p^*)$ where $p_*$ and $p^*$ are both asymptotically equal to $d/n$.\n  This famous conjecture was previously proved for all $d\\gg (n\\log n)^{3/4}$.\n  In this paper, we confirm the conjecture when $d \\gg \\log^4 n$. We also extend this result to near-regular degree sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09449","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/2011.09449/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"}