# A proof of menger's theorem by contraction

Discussiones Mathematicae Graph Theory (2002)

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

## Access Full Article

top## Abstract

top## How to cite

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

@article{FrankGöring2002,

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},

}

TY - JOUR

AU - Frank Göring

TI - A proof of menger's theorem by contraction

JO - Discussiones Mathematicae Graph Theory

PY - 2002

VL - 22

IS - 1

SP - 111

EP - 112

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.

LA - eng

KW - connectivity; disjoint paths; digraph; Menger; Menger theorem

UR - http://eudml.org/doc/270245

ER -

## References

top- [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] W. McCuaig, A simple proof of Menger's theorem, J. Graph Theory 8 (1984) 427-429, doi: 10.1002/jgt.3190080311. Zbl0545.05042
- [3] R. Diestel, Graph Theory (2nd edition), (Springer-Verlag, New York, 2000).
- [4] G.A. Dirac, Short proof of Menger's graph theorem, Mathematika 13 (1966) 42-44, doi: 10.1112/S0025579300004162. Zbl0144.45102
- [5] F. Goering, Short Proof of Menger's Theorem, to appear in Discrete Math.
- [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] K. Menger, Zur allgemeinen Kurventheorie, Fund. Math. 10 (1927) 96-115.
- [8] J.S. Pym, A proof of Menger's theorem, Monatshefte Math. 73 (1969) 81-88. Zbl0176.22502

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.