On circuits and serial symmetric basis-exchange in matroids
Combinatorics
2014-07-29 v6
Abstract
The way circuits, relative to a basis, are affected as a result of exchanging a basis element, is studied. As consequences, it is shown that three consecutive symmetric exchanges exist for any two bases of a matroid, and that a full serial symmetric exchange, of length at most 6, exists for any two bases of a matroid of rank 5. A new characterization of binary matroids, related to basis-exchange, is presented.
Cite
@article{arxiv.1110.5166,
title = {On circuits and serial symmetric basis-exchange in matroids},
author = {Daniel Kotlar},
journal= {arXiv preprint arXiv:1110.5166},
year = {2014}
}