Rota's Basis Conjecture for Matroids with Density Close to One
Combinatorics
2022-07-01 v3
Abstract
Rota's basis conjecture (RBC) states that given a collection B of n bases in a matroid M of rank n, one can always find n disjoint rainbow bases with respect to B. We show that if M is a matroid having n + k elements, then one can construct n - k^3 disjoint rainbow bases, where b is a constant depending only on k.
Keywords
Cite
@article{arxiv.2107.07024,
title = {Rota's Basis Conjecture for Matroids with Density Close to One},
author = {Sean McGuinness},
journal= {arXiv preprint arXiv:2107.07024},
year = {2022}
}