The structure of the 3–separations of 3–connected matroids
J. Oxley, C. Semple and G. Whittle
View Report [PDF - 297 KB]
Abstract
Tutte defined a k–separation of a matroid M to be a partition (A, B) of the ground set of M such that |A|, |B| ≥ k and r(A) + r(B) - r(M) < k. If, for all m < n, the matroid M has no m–separations, then M is n–connected. Earlier, Whitney showed that (A, B) is a 1–separation of M if and only if A is a union of 2–connected components of M. When M is 2–connected, Cunningham and Edmonds gave a tree decomposition of M that displays all of its 2–separations. When M is 3–connected, this paper describes a tree decomposition of M that displays, up to a certain natural equivalence, all non-trivial 3–separations of M.
Back to Research Reports
