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Extensions of Menger's Theorem

✍ Scribed by Dirac, G. A.

Book ID: 120098149
Publisher: Oxford University Press
Year: 1963
Tongue: English
Weight: 403 KB
Volume: s1-38
Category: Article
ISSN: 0024-6107
DOI: 10.1112/jlms/s1-38.1.148

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📜 SIMILAR VOLUMES

Menger's Theorem

✍ T. Böhme; F. Göring; J. Harant 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 47 KB

## 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

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This paper generalizes one of the celebrated results in Graph Theory due to Karl. A. Menger (1927), which plays a crucial role in many areas of flow and network theory. This paper also introduces and characterizes strength reducing sets of nodes and arcs in weighted graphs.

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A proof of Menger's theorem

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More proofs of menger's theorem

✍ C. St. J. A. Nash-Williams; W. T. Tutte 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 231 KB

## Abstract Four ways of proving Menger's Theorem by induction are described. Two of them involve showing that the theorem holds for a finite undirected graph __G__ if it holds for the graphs obtained from __G__ by deleting and contracting the same edge. The other two prove the directed version of