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- W4205817342 abstract "Abstract The bandwidth theorem of Böttcher, Schacht and Taraz states that any n -vertex graph G with minimum degree $big(tfrac{k-1}{k}+o(1)big)n$ contains all n -vertex k -colourable graphs H with bounded maximum degree and bandwidth o ( n ). Recently, a subset of the authors proved a random graph analogue of this statement: for $pgg big(tfrac{log n}{n}big)^{1/Delta}$ a.a.s. each spanning subgraph G of G ( n , p ) with minimum degree $big(tfrac{k-1}{k}+o(1)big)pn$ contains all n -vertex k -colourable graphs H with maximum degree $Delta$ , bandwidth o ( n ), and at least $C p^{-2}$ vertices not contained in any triangle. This restriction on vertices in triangles is necessary, but limiting. In this paper, we consider how it can be avoided. A special case of our main result is that, under the same conditions, if additionally all vertex neighbourhoods in G contain many copies of $K_Delta$ then we can drop the restriction on H that $Cp^{-2}$ vertices should not be in triangles." @default.
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- W4205817342 date "2021-12-13" @default.
- W4205817342 modified "2023-09-25" @default.
- W4205817342 title "A spanning bandwidth theorem in random graphs" @default.
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- W4205817342 doi "https://doi.org/10.1017/s0963548321000481" @default.
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