Hong Liu

activity

20242026

most citedBipartite Turán problems via graph gluing

1 citations · 1 across the 8 of their papers we have counts for

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4 papers · 1 filter

math.CO2024

Induced even cycles in locally sparse graphs

Laihao Ding, Jun Gao, Hong Liu +2

A graph $G$ is $(c, t)$ -sparse if for every pair of vertex subsets $A, B \subset V (G)$ with $∣ A ∣, ∣ B ∣ \geq t$ , $e (A, B) \leq (1 - c) ∣ A ∣∣ B ∣$ . In this paper we prove that for every $c > 0$ and…

math.CO2024

Sidorenko's conjecture for subdivisions and theta substitutions

Seonghyuk Im, Ruonan Li, Hong Liu

The famous Sidorenko's conjecture asserts that for every bipartite graph $H$ , the number of homomorphisms from $H$ to a graph $G$ with given edge density is minimized when $G$ is p…

math.CO2024

Generalized Ramsey--Turán density for cliques

Jun Gao, Suyun Jiang, Hong Liu +1

We study the generalized Ramsey--Turán function $RT (n, K_{s}, K_{t}, o (n))$ , which is the maximum possible number of copies of $K_{s}$ in an $n$ -vertex $K_{t}$ -free graph with indepe…

math.CO2024

Graph with any rational density and no rich subsets of linear size

Seonghyuk Im, Suyun Jiang, Hong Liu +1

A well-known application of the dependent random choice asserts that any $n$ -vertex graph $G$ with positive edge density contains a `rich' vertex subset $U$ of size $n^{1 - o (1)}$ su…