Tangles, trees, and flowers

  • Authors:

  • Ben Clark;Geoff Whittle

  • Affiliations:

  • -;-

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2013

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Abstract

A tangle of order k in a matroid or graph may be thought of as a ''k-connected component''. For a tangle of order k in a matroid or graph that satisfies a certain robustness condition, we describe a tree decomposition of the matroid or graph that displays, up to a certain natural equivalence, all the k-separations of the matroid or graph that are non-trivial with respect to the tangle.