论文标题
对扩展器的分区的评论
Remarks on partitions into expanders
论文作者
论文摘要
在本说明中，我们给出了一个简短的证明，表明没有线性小的Følner集的图可以分为扩展器的结合。我们用这个事实证明了一个图形的分区结果，该图形承认线性最大的最大følner集，我们推断出这样的图形家庭必须包含一个扩展器家族。我们还表明，分区中存在为扩展器是一种准偶然的不变。
In this note we give a short proof that graphs having no linearly small Følner sets can be partitioned into a union of expanders. We use this fact to prove a partition result for graphs admitting linearly small maximal Følner sets and we deduce that a family of such graphs must contain a family of expanders. We also show that the existence of partitions into expanders is a quasi-isometry invariant.
