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On 3-Connected Matroids
- Source :
- Canadian Journal of Mathematics. 33:20-27
- Publication Year :
- 1981
- Publisher :
- Canadian Mathematical Society, 1981.
-
Abstract
- 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.
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 33
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........b7306ef44d4bf490fdf567d152054f2c