{"paper":{"title":"On Koml\\'os' tiling theorem in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Nemanja \\v{S}kori\\'c, Rajko Nenadov","submitted_at":"2016-11-29T03:27:56Z","abstract_excerpt":"Conlon, Gowers, Samotij, and Schacht showed that for a given graph $H$ and a constant $\\gamma > 0$, there exists $C > 0$ such that if $p \\ge Cn^{-1/m_2(H)}$ then asymptotically almost surely every spanning subgraph $G$ of the random graph $\\mathcal{G}(n,p)$ with minimum degree at least $\\delta(G) \\ge (1 - 1/\\chi_{\\mathrm{cr}}(H) + \\gamma )np$ contains an $H$-packing that covers all but at most $\\gamma n$ vertices. Here, $\\chi_{\\mathrm{cr}}(H)$ denotes the critical chromatic threshold, a parameter introduced by Koml\\'os. We show that this theorem can be bootstraped to obtain an $H$-packing cove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09466","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":""},"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"}