Ting-Wei Chao

collaborators

3 papers

math.CO2024

Empty red-red-blue triangles

Ting-Wei Chao, Zichao Dong, Zhuo Wu

Let $P$ be a $2 n$ -point set in the plane that is in general position. We prove that every red-blue bipartition of $P$ into $R$ and $B$ with $∣ R ∣ = ∣ B ∣ = n$ generates $Ω (n^{3/2})$ r…

math.CO2020

Empty axis-parallel boxes

Boris Bukh, Ting-Wei Chao

We show that, for every set of $n$ points in the $d$ -dimensional unit cube, there is an empty axis-parallel box of volume at least $Ω (d / n)$ as $n \to \infty$ and $d$ is fixed. In the…

math.CO2020

On convex holes in $d$ -dimensional point sets

Boris Bukh, Ting-Wei Chao, Ron Holzman

Given a finite set $A \subseteq R^{d}$ , points $a_{1}, a_{2}, \dots, a_{ℓ} \in A$ form an $ℓ$ -hole in $A$ if they are the vertices of a convex polytope which contains no poi…

Empty red-red-blue triangles

Empty axis-parallel boxes

On convex holes in d-dimensional point sets

On convex holes in $d$ -dimensional point sets