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Set Systems with Covering Properties and Low VC-Dimension

2024/01/20 by Peterzil, George, Steinmeyer, Johanna · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.12252

Abstract

Given natural numbers k ≤ s ≤ n, we ask: what is the minimal VC-dimension of a family 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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