Decomposition of 3-connected representable matroids

作者:Chen Rong*; Xiang Kai nan
来源:Journal of Combinatorial Theory - Series B, 2012, 102(3): 647-670.
DOI:10.1016/j.jctb.2011.09.006

摘要

In this paper, we prove that via an operation "reducing", every 3-connected representable matroid M with at least nine elements can be decomposed into a set of sequentially 4-connected matroids and three special matroids which we call freely-placed-line matroids, spike-like matroids and swirl-like matroids; more concretely, there is a labeled tree that gives a precise description of the way that M built from its pieces.

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