论文标题
quasirandom超图的分解为有限程度的超图
Decompositions of quasirandom hypergraphs into hypergraphs of bounded degree
论文作者
论文摘要
我们证明，任何Quasirandom统一超graph $ h $都可以大约分解为任何边缘几乎相当多的有界度超图的集合。实际上，我们的结果也适用于多部分超图，甚至适用于稀疏的设置，当$ h $的密度迅速倾向于$ 0 $ $ 0 $。我们的结果回答并解决了Kim，Kühn，Osthus和Tyomkyn的问题；以及格洛克（Glock），库恩（Kühn）和奥斯图斯（Osthus）以及凯瓦什（Keevash）。 所提供的近似分解具有强大的quasirandom特性，对于即将到来的应用非常有用。我们的结果还暗示了对长期图形分解问题的天然超图版本的近似解决方案，以及（准）随机简单复合物的几个分解结果分解为各种基本的简单络合物，例如球体的三角剖分和其他歧管。
We prove that any quasirandom uniform hypergraph $H$ can be approximately decomposed into any collection of bounded degree hypergraphs with almost as many edges. In fact, our results also apply to multipartite hypergraphs and even to the sparse setting when the density of $H$ quickly tends to $0$ in terms of the number of vertices of $H$. Our results answer and address questions of Kim, Kühn, Osthus and Tyomkyn; and Glock, Kühn and Osthus as well as Keevash. The provided approximate decompositions exhibit strong quasirandom properties which is very useful for forthcoming applications. Our results also imply approximate solutions to natural hypergraph versions of long-standing graph decomposition problems, as well as several decomposition results for (quasi)random simplicial complexes into various more elementary simplicial complexes such as triangulations of spheres and other manifolds.
