Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-06-08T15:25:26.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Matchings in Countable Graphs

Published online by Cambridge University Press:  20 November 2018

K. Steffens
K. Steffens*
Affiliation:
Technische Universität Hannover, Hannover, West Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Tutte [9] has given necessary and sufficient conditions for a finite graph to have a perfect matching. Different proofs are given by Brualdi [1] and Gallai [2; 3]. The shortest proof of Tutte's theorem is due to Lovasz [5]. In another paper [10] Tutte extended his conditions for a perfect matching to locally finite graphs. In [4] Kaluza gave a condition on arbitrary graphs which is entirely different from Tutte's.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 165 - 168
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Brualdi, R. A., Matchings in arbitrary graphs, Proc. Camb. Phil. Soc. 69 (1971), 401–407.Google Scholar
2. Gallai, T., On factorisation of graphs, Acta Math. Acad. Sci. Hungar. 1 (1950), 133–152.Google Scholar
3. Gallai, T. Neuer Beweis eines Tutte'schen Satzes, Magyar Tud. Akad. Mat. Kutato Int. Kôzl. 8 (1963), 135–139.Google Scholar
4. Kaluza, Th., Ein Kriterium fiir das Vorhandensein von Faktoren in beliebigen Graphen, Math. Ann. 126 (1953), 464–465 Google Scholar
5. Lovasz, L., Three short proofs in graph theory, J. Combinatorial Theory (B) 19 (1975), 269- 271Google Scholar
6. Podeski, K. P. and Steffens, K., Infective choice functions, J. Combinatorial Theory (B) 21 (1976), 40–46.Google Scholar
7. Rado, R., Axiomatic treatment of rank in infinite sets, Can. J. Math. 1 (1949), 337–343.Google Scholar
8. Steffens, K., Ergebnisse aus der Transversalentheorie I, J. Combinatorial Theory (A) 20 (1976), 187–201.Google Scholar
9. Tutte, W. T., The factorization of linear graphs, J. London Math. Soc. 22 (1947), 107–111.Google Scholar
10. Tutte, W. T. The factorization of locally finite graphs, Can. J. Math. 2 (1950), 44–49.Google Scholar