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Applications of Menger's graph theorem

✍ Scribed by Hazel Perfect


Publisher
Elsevier Science
Year
1968
Tongue
English
Weight
844 KB
Volume
22
Category
Article
ISSN
0022-247X

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## Abstract A well‐known conjecture of ErdΕ‘s states that given an infinite graph __G__ and sets __A__,β€‰βŠ†β€‰__V__(__G__), there exists a family of disjoint __A__β€‰βˆ’β€‰__B__ paths 𝓅 together with an __A__β€‰βˆ’β€‰__B__ separator __X__ consisting of a choice of one vertex from each path in 𝓅. There is a natural

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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