Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-16T15:42:56.547Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Number of Disjoint Edges in a Graph

Published online by Cambridge University Press:  20 November 2018

Joseph M. Weinstein
Joseph M. Weinstein*
Affiliation:
University of Wisconsin
Rights & Permissions [Opens in a new window]

Extract

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.

In what follows we prove that a finite graph of n nodes in which each node has degree ≥ 1 but ≤ possesses a set of at least n/(1 + ) pairwise disjoint edges. Our principal theorem states an analogue of this result for the case when each node has degree ≥2: we show that in this case the graph possesses a set of at least 2n/(2 + max(4, )) mutually disjoint edges.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 106 - 111
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. K, D.ônig, Théorie der endlichen und unendlichen Graphen, Leipzig (1936); Chelsea, New York (1950).Google Scholar
2. Dirac, G., Map colour theorems related to the Heawood colour formula (I), J. London Math. Soc, 81 (1956), 460–471.Google Scholar