Triads and triangles in 3-connected matroids Original Research Article

This paper generalizes a result of Mader for graphs by proving that if f is an element of a circuit C of a 3-connected matroid M and M⧹e is not 3-connected for each e ϵ C − {f}, then C meets a triad of M. Several consequences of this result are proved. One of these generalizes a graph result of Wu. The others provide 3-connected analogues of 2-connected matroid results of Oxley.