The uniform Tur\'an density of large stars

TL;DR

This paper determines the exact uniform Turán density for large stars in hypergraphs, confirming a conjecture for all sufficiently large stars and matching previous lower bounds.

Contribution

We asymptotically resolve the uniform Turán density for large stars, establishing the exact value for all sufficiently large k, extending prior partial results.

Findings

Uniform Turán density of large stars is rac{k^2-5k+7}{(k-1)^2} for k  48

Matches the lower bound construction by Reiher, R46dl, and Schacht

Provides a complete asymptotic solution for the problem for large k.

Abstract

We asymptotically resolve the the uniform Tur\'an density problem for the large stars. In particular, we show that the uniform Tur\'an density of the $k$-star $S_k$ is $\frac{k^2-5k+7}{(k-1)^2}$ for $k\ge 48$, matching a lower construction by Reiher, R\"odl and Schacht.