Zichao Dong

collaborators

3 papers

math.CO2025

Convex polytopes in restricted point sets in $R^{d}$

Boris Bukh, Zichao Dong

For a finite point set $P \subset R^{d}$ , denote by $diam (P)$ the ratio of the largest to the smallest distances between pairs of points in $P$ . Let $c_{d, I^\pm} (n)$ be…

math.CO2024

Many cliques with small degree powers

Ting-Wei Chao, Zichao Dong, Zijun Shen +1

Suppose $0 < p \leq \infty$ . For a simple graph $G$ with a vertex-degree sequence $d_{1}, \dots, d_{n}$ satisfying $(d_{1}^{p} + \dots + d_{n}^{p})^{1/ p} \leq C$ , we prove asymptotically sharp u…

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 $I^c ◯ (n^{3/2})$ …

Convex polytopes in restricted point sets in Rd

Many cliques with small degree powers

Empty red-red-blue triangles

Convex polytopes in restricted point sets in $R^{d}$