Hao-tian Liu

collaborators

3 papers

math.CO2026

A Quadratic Vertex Threshold for Isolated Cliques in the Minimum Degree Kruskal-Katona Problem for 3-Uniform Hypergraphs

Haorui Liu, Mei Lu, Yi Zhang

Given a set $X$ and an integer $t$ , let $F$ be a family of $k$ -subsets of $X$ . The Kruskal-Katona theorem states that if $∣ F ∣ \geq (k t)$ , then $|\partial…

math.CO2026

Shadows of Uniform Hypergraphs under a Minimum Degree Condition

Haorui Liu, Mei Lu, Yi Zhang

Given a set $X$ and an integer $t$ , let $F$ be a family of $k$ -subsets of $X$ . The Kruskal--Katona theorem implies that if $∣ F ∣ \geq (k t)$ , then $|\parti…

math.CO2025

Vertex degree sums for rainbow matchings in 3-uniform hypergraphs

Haorui Liu, Mei Lu, Yan Wang +1

Let $n \in 3 Z$ be sufficiently large. Zhang, Zhao and Lu proved that if $H$ is a 3-uniform hypergraph with $n$ vertices and no isolated vertices, and if $deg(u)+deg(v) > \…