Set Systems with Covering Properties and Low VC-Dimension

George Peterzil; Johanna Steinmeyer

doi:10.1007/s00373-025-02922-9

Set Systems with Covering Properties and Low VC-Dimension

George Peterzil
, Johanna Steinmeyer^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	68
Journal	Graphs and Combinatorics
Volume	41
Issue number	3
DOIs	https://doi.org/10.1007/s00373-025-02922-9
State	Published - Jun 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Keywords

Set system
VC-dimension

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10.1007/s00373-025-02922-9

Cite this

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Set Systems with Covering Properties and Low VC-Dimension

Abstract

Bibliographical note

Keywords

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