Zichao Dong

activity

20202024

most citedOn the stability of graph independence number

2 citations · 4 across the 7 of their papers we have counts for

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6 papers · 1 filter

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 $Ω (n^{3/2})$ r…

math.CO2022★ 1 cited

Rainbow even cycles

Zichao Dong, Zijian Xu

We prove that every family of (not necessarily distinct) even cycles $D_{1}, \dots, D_{⌊ 1.2 (n - 1)⌋ + 1}$ on some fixed $n$ -vertex set has a rainbow even cycle (that is, a…

math.CO2022

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 $c_{d, α} (n)$ be…

math.CO2022★ 1 cited

A simple proof of the Gan-Loh-Sudakov conjecture

Ting-Wei Chao, Zichao Dong

We give a new unified proof that any simple graph on $n$ vertices with maximum degree at most $Δ$ has no more than $a (t Δ + 1) + (t b)$ cliques of size $t (t \geq 3)$ , w…

math.CO2021★ 2 cited

On the stability of graph independence number

Zichao Dong, Zhuo Wu

Let $G$ be a graph on $n$ vertices of independence number $α (G)$ such that every induced subgraph of $G$ on $n - k$ vertices has an independent set of size at least $α (G) - ℓ$ . Wh…