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On 3-Connected Matroids

Published online by Cambridge University Press:  20 November 2018

James G. Oxley
James G. Oxley*
Affiliation:
Australian National University, Canberra, Australia
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This paper extends several graph-theoretic results to matroids. The main result of Tutte's paper [10] which introduced the theory of n-connection for matroids was a generalization of an earlier result of his [9] for 3-connected graphs. The latter has since been strengthened by Halin [3] and in Section 3 of this paper we prove a matroid analogue of Halin's result. Tutte used his result for 3-connected graphs to deduce a recursive construction of all simple 3-connected graphs having at least four vertices. In Section 4 we generalize this by giving a recursive construction of all 3-connected matroids of rank at least three. Section 2 contains a generalization to minimally n-connected matroids of a result of Dirac [2] for minimally 2-connected graphs.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 1 , 01 February 1981 , pp. 20 - 27
Copyright
Copyright © Canadian Mathematical Society 1981

References

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