## Abstract A well‐known conjecture of Erdős states that given an infinite graph __G__ and sets __A__, ⊆ __V__(__G__), there exists a family of disjoint __A__ − __B__ paths 𝓅 together with an __A__ − __B__ separator __X__ consisting of a choice of one vertex from each path in 𝓅. There is a natural
✦ LIBER ✦
Menger’s theorem for infinite graphs
✍ Scribed by Ron Aharoni; Eli Berger
- Publisher
- Springer-Verlag
- Year
- 2008
- Tongue
- English
- Weight
- 654 KB
- Volume
- 176
- Category
- Article
- ISSN
- 0020-9910
No coin nor oath required. For personal study only.
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## Abstract Menger's Theorem for digraphs states that for any two vertex sets __A__ and __B__ of a digraph __D__ such that __A__ cannot be separated from __B__ by a set of at most __t__ vertices, there are __t + 1__ disjoint __A__–__B__‐paths in __D__. Here a short and elementary proof of a more ge