An obstacle to a decomposition theorem for near-regular matroids
Combinatorics
2015-03-13 v3
Abstract
Seymour's Decomposition Theorem for regular matroids states that any matroid representable over both GF(2) and GF(3) can be obtained from matroids that are graphic, cographic, or isomorphic to R10 by 1-, 2-, and 3-sums. It is hoped that similar characterizations hold for other classes of matroids, notably for the class of near-regular matroids. Suppose that all near-regular matroids can be obtained from matroids that belong to a few basic classes through k-sums. Also suppose that these basic classes are such that, whenever a class contains all graphic matroids, it does not contain all cographic matroids. We show that in that case 3-sums will not suffice.
Keywords
Cite
@article{arxiv.0905.3252,
title = {An obstacle to a decomposition theorem for near-regular matroids},
author = {Dillon Mayhew and Geoff Whittle and Stefan H. M. van Zwam},
journal= {arXiv preprint arXiv:0905.3252},
year = {2015}
}
Comments
11 pages, 1 figure