VC-saturated set systems - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

VC-saturated set systems

Résumé

The well-known Sauer lemma states that a family $\mathcal{F}\subseteq 2^{[n]}$ of VC-dimension at most $d$ has size at most $\sum_{i=0}^d\binom{n}{i}$. We obtain both random and explicit constructions to prove that the corresponding saturation number, i.e., the size of the smallest maximal family with VC-dimension $d\ge 2$, is at most $4^{d+1}$, and thus is independent of $n$.

Dates et versions

hal-03236576 , version 1 (26-05-2021)

Identifiants

Citer

Aresenii Sagdeev, Nóra Frankl, Sergei Kiselev, Andrey Kupavskii, Balázs Patkós. VC-saturated set systems. 2021. ⟨hal-03236576⟩
27 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More