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arXiv · 2604.17595

Fundamental cycles in grid graphs

Bartłomiej Kielak·Daniel Král'·Ander Lamaison·Xichao Shu
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Abstract

We show that the average length of a fundamental cycle with respect to any fixed spanning tree of the $n\times n$ square grid is at least $Ω(\log n)$; the bound is asymptotically tight. This result answers in the affirmative a question posed by McCarty in relation to sparse representations of binary matroids.

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Bartłomiej Kielak, Daniel Král', Ander Lamaison, Xichao Shu. 2026-08-11. Fundamental cycles in grid graphs. https://arxiv.org/abs/2604.17595

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