The structure of the 3-separations of 3-connected matroids II

@article{Oxley2007TheSO,
  title={The structure of the 3-separations of 3-connected matroids II},
  author={James G. Oxley and Charles Semple and Geoff Whittle},
  journal={Eur. J. Comb.},
  year={2007},
  volume={28},
  pages={1239-1261}
}
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 M has no (n − 1)–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… CONTINUE READING

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A combinatorial decomposition theory, Canad

  • W. H. Cunningham, J. Edmonds
  • J. Math
  • 1980
Highly Influential
3 Excerpts

The structure of equivalent 3 - separations in a 3 - connected matroid

  • R. Hall, J. Oxley, C. Semple
  • Adv . Appl . Math .
  • 2005

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