Matroids with at least two regular elements
Combinatorics
2015-09-15 v1
Abstract
For a matroid , an element such that both and are regular is called a regular element of . We determine completely the structure of non-regular matroids with at least two regular elements. Besides four small size matroids, all 3-connected matroids in the class can be pieced together from or and a regular matroid using 3-sums. This result takes a step toward solving a problem posed by Paul Seymour: Find all 3-connected non-regular matroids with at least one regular element [5, 14.8.8].
Keywords
Cite
@article{arxiv.1103.2959,
title = {Matroids with at least two regular elements},
author = {Sandra Kingan and Manoel Lemos},
journal= {arXiv preprint arXiv:1103.2959},
year = {2015}
}