Discussiones Mathematicae Graph Theory 22(1) (2002) 111-112
doi: 10.7151/dmgt.1161

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A PROOF OF MENGER'S THEOREM BY CONTRACTION

Frank Göring

Department of Mathematics
Technical University of Ilmenau
D-98684 Ilmenau Germany

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.

Keywords: connectivity, disjoint paths, digraph, Menger.

2000 Mathematics Subject Classifications: 05C40.

References

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[4] G.A. Dirac, Short proof of Menger's graph theorem, Mathematika 13 (1966) 42-44, doi: 10.1112/S0025579300004162.
[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.
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Received 8 June 2000
Revised 21 May 2001