图中的瓶颈化与一个粗化Menger型定理
Bottlenecking in graphs and a coarse Menger-type theorem
AI总结：
本文扩展瓶颈化概念并提出粗化瓶颈化，据此证明粗化Menger型定理并提出粗化Erdős-Menger型猜想，为图的连通性粗化度量提供新路径。
摘要：
我们扩展了早期工作中引入的瓶颈化概念，刻画了一类图谱，并证明这自然地延伸为粗化瓶颈化的概念。我们展示了瓶颈化概念如何为连通性的粗化度量提供一种不同于粗化Menger猜想的进路，该猜想由Georgakopoulos和Papasoglu以及Albrechtsen、Huynh、Jacobs、Knappe和Wollan分别独立提出，且最近被一个反例所否定。我们陈述并证明了一个粗化Menger型定理，并且本着Erdős-Menger猜想的精神——该猜想在数十年后被Aharoni和Berger证明——提出了一个粗化Erdős-Menger型猜想。
英文摘要：
We expand upon the notion of bottlenecking introduced in our earlier work, characterizing a spectrum of graphs and showing that this naturally extends to a concept of coarse bottlenecking. We show how the notion of bottlenecking provides a different approach to coarsening measures of connectedness than the Coarse Menger Conjecture proposed independently by Georgakopoulos and Papasoglu as well as Albrechtsen, Huynh, Jacobs, Knappe, and Wollan - which was recently disproved by a counterexample. We formulate and prove a Coarse Menger-type theorem, and also propose a coarse Erdős-Menger-type Conjecture, in the spirit of the Erdős-Menger conjecture which was proven after decades by Aharoni and Berger.
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