Cyclic Orderings of Paving Matroids
Combinatorics
2024-08-06 v2
Abstract
A matroid M is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miyano, and Ueno states that a matroid M is cyclically orderable if and only if for all nonempty subsets X in E(M), |X|/r(M) is less than or equal to |E(M)|/r(M). In this paper, we verify this conjecture for all paving matroids.
Keywords
Cite
@article{arxiv.2308.12239,
title = {Cyclic Orderings of Paving Matroids},
author = {Sean McGuinness},
journal= {arXiv preprint arXiv:2308.12239},
year = {2024}
}