The authors showed in an earlier paper that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid. The purpose of this paper is to show that if certain natural conditions are imposed on the tree, then it has a uniqueness property. In particular, suppose that, from every pair of edges that meet at a degree-2 vertex and have their other ends of degree at least three, one edge is contracted. Then the resulting tree is unique. © 2006 Elsevier Ltd. All rights reserved.
Publication Source (Journal or Book title)
European Journal of Combinatorics
Oxley, J., Semple, C., & Whittle, G. (2007). The structure of the 3-separations of 3-connected matroids II. European Journal of Combinatorics, 28 (4), 1239-1261. https://doi.org/10.1016/j.ejc.2006.01.007