Geodesic
On 3-Connected Matroids
Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 20-27

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Oxley, James G. On 3-Connected Matroids. Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 20-27. doi: 10.4153/CJM-1981-003-9
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