The comments below apply to all printings of the book dated 2005 or earlier. The table following contains more than just a list of typing errors. Some statements and proofs have been corrected,â€¦ (More)

We prove that, for every positive integer k, there is an integer N such that every 3-connected graph with at least N vertices has a minor isomorphic to the k-spoke wheel or K3,k; and that everyâ€¦ (More)

Kahn conjectured in 1988 that, for each prime power q, there is an integer n(q) such that no 3-connected GF(q)-representable matroid has more than n(q) inequivalent GF(q)-representations. At theâ€¦ (More)

Tutte defined a kâ€“separation of a matroid M to be a partition (A, B) of the ground set of M such that |A|, |B| â‰¥ k and r(A) + r(B) âˆ’ r(M) < k. If, for all m < n, the matroid M has no mâ€“separations,â€¦ (More)

In this paper we derive several results for connected matroids and use these to obtain new results for 2-connected graphs. In particular, we generalize work of Murty and Seymour on the number ofâ€¦ (More)

The authors showed in an earlier paper that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid. The purpose of this paper is to showâ€¦ (More)

Let F be a field and let N be a matroid in a class N of F-representable matroids that is closed under minors and the taking of duals. Then N is an F-stabilizer for N if every representation of aâ€¦ (More)