## 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
Menger's Theorem
✍ Scribed by T. Böhme; F. Göring; J. Harant
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 47 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0364-9024
- DOI
- 10.1002/jgt.1001
No coin nor oath required. For personal study only.
✦ Synopsis
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 general theorem is given. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 35–36, 2001
📜 SIMILAR VOLUMES
## Abstract A new proof of Menger's theorem is presented.
## Abstract A proof of Menger's theorem is presented.
## 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
An edge-scheduled network N is a multigraph G = (V, E), where each edge e E E has been assigned two real weights: a start time a(e) and a finish time p(e). Such a multigraph models a communication or transportation network. A multiedge joining vertices u and v represents a direct communication (tran