The structure of crossing separations in matroids
Oxley, Semple and Whittle described a tree decomposition for a 3-connected matroid M that displays, up to a natural equivalence, all non-trivial 3-separations of M. Crossing 3-separations gave rise to fundamental structures known as flowers. In this paper, we define a generalized flower structure called a k-flower, with no assumptions on the connectivity of M. We completely classify k-flowers in terms of the local connectivity between pairs of petals. © 2007 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Advances in Applied Mathematics
Aikin, J., & Oxley, J. (2008). The structure of crossing separations in matroids. Advances in Applied Mathematics, 41 (1), 10-26. https://doi.org/10.1016/j.aam.2007.05.004