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Matchings in graphs

Published online by Cambridge University Press:  17 April 2009

P.J. McCarthy
P.J. McCarthy
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas, USA.
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Abstract

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Results of Tutte and of Anderson giving conditions for a simple graph G to have a perfect matching are generalized to give conditions for G to have a matching of defect d. A corollary to one of these results is a theorem of Berge on the size of a maximum matching in G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 1 , August 1973 , pp. 141 - 143
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Anderson, Ian, “Perfect matchings of a graph”, J. Combinatorial Theory Ser. B 10 (1971), 183–186.CrossRefGoogle Scholar
[2]Berge, Claude, “Sur le couplage maximum d'un graphe”, C.R. Acad. Sci. Paris 247 (1958), 258–259.Google Scholar
[3]Berge, Claude, The theory of graphe and its applications (translated by Methuen, Alison Doig, London; John Wiley & Sons, New York, 1962).Google Scholar
[4]Tutte, W.T., “The factorization of linear graphs”, J. London Math. Soc. 22 (1947), 107–111.CrossRefGoogle Scholar