Fundamental cycles in grid graphs
Combinatorics
2026-04-21 v1
Abstract
We show that the average length of a fundamental cycle with respect to any fixed spanning tree of the square grid is at least ; the bound is asymptotically tight. This result answers in the affirmative a question posed by McCarty in relation to sparse representations of binary matroids.
Keywords
Cite
@article{arxiv.2604.17595,
title = {Fundamental cycles in grid graphs},
author = {Bartłomiej Kielak and Daniel Král' and Ander Lamaison and Xichao Shu},
journal= {arXiv preprint arXiv:2604.17595},
year = {2026}
}