The bandwidth theorem of Böttcher, Schacht, and Taraz [Proof of the bandwidth conjecture of Bollobás andKomlós, Mathematische Annalen, 2009] gives a condition on the minimum degree of an n-vertex graph G that ensures G contains every r-chromatic graph H on n vertices of bounded degree and of bandwidth $o(n)$ , thereby proving a conjecture of Bollobás and Komlós [The Blow-up Lemma, Combinatorics, Probability, and Computing, 1999]. In this paper, we prove a version of the bandwidth theorem for locally dense graphs. Indeed, we prove that every locally dense n-vertex graph G with $\delta (G)> (1/2+o(1))n$ contains as a subgraph any given (spanning) H with bounded maximum degree and sublinear bandwidth.

中文翻译：

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局部密集图的带宽定理

这带宽定理Böttcher、Schacht 和 Taraz [Bollobás 带宽猜想的证明和Komlós，数学年鉴，2009] 给出了一个最小度数的条件n-顶点图G确保G包含每个r-彩色图H在n有界度和带宽的顶点 $o(n)$ , 从而证明了 Bollobás 和 Komlós 的猜想 [爆炸引理，组合学、概率和计算，1999]。在本文中，我们证明了带宽定理的一个版本局部密集图表。确实，我们证明了每一个局部密集的n-顶点图G和 $\delta (G)> (1/2+o(1))n$ 包含作为子图的任何给定（跨越）H有界最大度数和次线性带宽。