Hong Liu

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20242026

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3 papers · 1 filter

math.CO2024

Clique density vs blowups

Domagoj Bradač, Hong Liu, Zhuo Wu +1

A well-known theorem of Nikiforov asserts that any graph with a positive $K_{r}$ -density contains a logarithmic blowup of $K_{r}$ . In this paper, we explore variants of Nikiforov's r…

math.CO2024

Piercing independent sets in graphs without large induced matching

Jiangdong Ai, Hong Liu, Zixiang Xu +1

Given a graph $G$ , denote by $h (G)$ the smallest size of a subset of $V (G)$ which intersects every maximum independent set of $G$ . We prove that any graph $G$ without induced match…

math.CO2024

Beyond chromatic threshold via the $(p, q)$ -theorem, and a sharp blow-up phenomenon

Hong Liu, Chong Shangguan, Jozef Skokan +1

We establish a novel connection between the well-known chromatic threshold problem in extremal combinatorics and the celebrated $(p, q)$ -theorem in discrete geometry. In particular,…

Clique density vs blowups

Piercing independent sets in graphs without large induced matching

Beyond chromatic threshold via the (p,q)-theorem, and a sharp blow-up phenomenon

Beyond chromatic threshold via the $(p, q)$ -theorem, and a sharp blow-up phenomenon