A proof of menger's theorem by contraction
Discussiones Mathematicae Graph Theory (2002)
- Volume: 22, Issue: 1, page 111-112
- ISSN: 2083-5892
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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
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