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- W4300792982 abstract "A perfect $H$-tiling in a graph $G$ is a collection of vertex-disjoint copies of a graph $H$ in $G$ that together cover all the vertices in $G$. In this paper we investigate perfect $H$-tilings in a random graph model introduced by Bohman, Frieze and Martin in which one starts with a dense graph and then adds $m$ random edges to it. Specifically, for any fixed graph $H$, we determine the number of random edges required to add to an arbitrary graph of linear minimum degree in order to ensure the resulting graph contains a perfect $H$-tiling with high probability. Our proof utilises Szemer'edi's Regularity lemma as well as a special case of a result of Koml'os concerning almost perfect $H$-tilings in dense graphs." @default.
- W4300792982 created "2022-10-04" @default.
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- W4300792982 date "2017-08-30" @default.
- W4300792982 modified "2023-09-23" @default.
- W4300792982 title "Tilings in randomly perturbed dense graphs" @default.
- W4300792982 doi "https://doi.org/10.48550/arxiv.1708.09243" @default.
- W4300792982 hasPublicationYear "2017" @default.
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