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- W4302064980 abstract "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 covering all but at most $gamma (C/p)^{m_2(H)}$ vertices, which is strictly smaller when $p > C n^{-1/m_2(H)}$. In the case where $H = K_3$ this answers the question of Balogh, Lee, and Samotij. Furthermore, we give an upper bound on the size of an $H$-packing for certain ranges of $p$." @default.
- W4302064980 created "2022-10-06" @default.
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- W4302064980 date "2016-11-28" @default.
- W4302064980 modified "2023-10-14" @default.
- W4302064980 title "On Koml'os' tiling theorem in random graphs" @default.
- W4302064980 doi "https://doi.org/10.48550/arxiv.1611.09466" @default.
- W4302064980 hasPublicationYear "2016" @default.
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