Decomposition of 3-connected representable matroids

Authors:
Rong Chen;Kai-nan Xiang
Affiliations:
Center for Discrete Mathematics, Fuzhou University, Fuzhou City, 350003, PR China;School of Mathematical Sciences, LPMC, Nankai University, Tianjin City, 300071, PR China
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

Citing 3
Cited 0

On inequivalent representations of matroids over finite fields

Journal of Combinatorial Theory Series B
The structure of the 3-separations of 3-connected matroids

Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
The structure of the 3-separations of 3-connected matroids II

European Journal of Combinatorics

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Abstract

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.