A proof of menger's theorem by contraction

Frank Göring

Discussiones Mathematicae Graph Theory (2002)

  • Volume: 22, Issue: 1, page 111-112
  • ISSN: 2083-5892

Abstract

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A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite graph for two subsets A and B of its vertex set is given. The main idea of the proof is to contract an edge of the graph.

How to cite

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Frank Göring. "A proof of menger's theorem by contraction." Discussiones Mathematicae Graph Theory 22.1 (2002): 111-112. <http://eudml.org/doc/270245>.

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abstract = {A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite graph for two subsets A and B of its vertex set is given. The main idea of the proof is to contract an edge of the graph.},
author = {Frank Göring},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {connectivity; disjoint paths; digraph; Menger; Menger theorem},
language = {eng},
number = {1},
pages = {111-112},
title = {A proof of menger's theorem by contraction},
url = {http://eudml.org/doc/270245},
volume = {22},
year = {2002},
}

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AU - Frank Göring
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JO - Discussiones Mathematicae Graph Theory
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AB - A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite graph for two subsets A and B of its vertex set is given. The main idea of the proof is to contract an edge of the graph.
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References

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  1. [1] T. Böhme, F. Göring and J. Harant, Menger's Theorem, J. Graph Theory 37 (2001) 35-36, doi: 10.1002/jgt.1001. Zbl0988.05057
  2. [2] W. McCuaig, A simple proof of Menger's theorem, J. Graph Theory 8 (1984) 427-429, doi: 10.1002/jgt.3190080311. Zbl0545.05042
  3. [3] R. Diestel, Graph Theory (2nd edition), (Springer-Verlag, New York, 2000). 
  4. [4] G.A. Dirac, Short proof of Menger's graph theorem, Mathematika 13 (1966) 42-44, doi: 10.1112/S0025579300004162. Zbl0144.45102
  5. [5] F. Goering, Short Proof of Menger's Theorem, to appear in Discrete Math. 
  6. [6] T. Grünwald (later Gallai), Ein neuer Beweis eines Mengerschen Satzes, J. London Math. Soc. 13 (1938) 188-192, doi: 10.1112/jlms/s1-13.3.188. Zbl0019.23701
  7. [7] K. Menger, Zur allgemeinen Kurventheorie, Fund. Math. 10 (1927) 96-115. 
  8. [8] J.S. Pym, A proof of Menger's theorem, Monatshefte Math. 73 (1969) 81-88. Zbl0176.22502

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