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arXiv · 2401.12252

Set Systems with Covering Properties and Low VC-Dimension

George Peterzil·Johanna Steinmeyer
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Abstract

Given natural numbers $k \leq s \leq n$, we ask: what is the minimal VC-dimension of a family $\mathcal{F}$ of $s$-subsets of $[n]$ that covers all $k$-subsets of $[n]$? We first show that for sufficiently large $n$ this number is always $k$, and construct families which give a lower bound for the actual growth of this stabilization point.

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George Peterzil, Johanna Steinmeyer. 2024-01-20. Set Systems with Covering Properties and Low VC-Dimension. https://arxiv.org/abs/2401.12252

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