{"paper":{"title":"Almost-spanning universality in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asaf Ferber, David Conlon, Nemanja \\v{S}kori\\'c, Rajko Nenadov","submitted_at":"2015-03-18T23:16:21Z","abstract_excerpt":"A graph $G$ is said to be $\\mathcal H(n,\\Delta)$-universal if it contains every graph on $n$ vertices with maximum degree at most $\\Delta$. It is known that for any $\\varepsilon > 0$ and any natural number $\\Delta$ there exists $c > 0$ such that the random graph $G(n,p)$ is asymptotically almost surely $\\mathcal H((1-\\varepsilon)n,\\Delta)$-universal for $p \\geq c (\\log n/n)^{1/\\Delta}$. Bypassing this natural boundary, we show that for $\\Delta \\geq 3$ the same conclusion holds when $p = \\omega\\left(n^{-\\frac{1}{\\Delta-1}}\\log^5 n\\right)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05612","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":""},"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"}