The structure of the 3-separations of 3-connected matroids (2004)
AuthorsOxley, J., Semple, C., Whittle, G.show all
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.
CitationOxley, J., Semple, C., Whittle, G. (2004) The structure of the 3-separations of 3-connected matroids. Journal of Combinatorial Theory, Series B, 92(2), pp. 257-293.
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