The structure of the 3-separations of 3-connected matroids II
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Journal Article
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University of Canterbury. Mathematics and Statistics.
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2007
Authors
Oxley, J.
Semple, C.
Whittle, G.
Abstract
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.
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Oxley, 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.