The structure of the 3-separations of 3-connected matroids II (2007)
AuthorsOxley, J., Semple, C., Whittle, G.show all
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.
CitationOxley, J., Semple, C., Whittle, G. (2007) The structure of the 3-separations of 3-connected matroids II. European Journal of Combinatorics, 28(4), pp. 1239-1261.
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