Largest $3$-uniform set systems with VC-dimension $2$
Jian Wang, Zixiang Xu, Shengtong Zhang
TL;DR
This paper determines the maximum size of 3-uniform set systems with VC-dimension 2 for all values of n, providing a complete characterization of their largest possible sizes.
Contribution
It provides a complete characterization of the largest 3-uniform set systems with VC-dimension 2 for all n, solving an open combinatorial problem.
Findings
Exact maximum sizes for all n.
Characterization of extremal set systems.
Resolution of a previously open problem.
Abstract
We determine the largest size of -uniform set systems on with VC-dimension for all .
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Mathematical Dynamics and Fractals