Haoran Luo

activity

20242026

collaborators

8 papers

math.CO2026

On the minimum size of maximal $k$ -wise intersecting families

Haoran Luo

A family $F$ of subsets of $[n] := {1, 2, \dots, n}$ is called maximal $k$ -wise intersecting if every collection of at most $k$ members of $F$ has a non-empty…

math.CO2026

Local maximum of inducibility profiles

JÃ³zsef Balogh, Bernard LidickÃ½, Haoran Luo

For a graph $G$ and $e \in [0, 1]$ , denote by $I_{G} (e)$ the supremum of induced density of $G$ over $n$ -vertex graphs with edge density $e$ as $n$ goes to infinity. Liu, Mubayi and Re…

math.CO2026

On the maximum density of $r$ -graphs in which every $(r + 1)$ -set spans $0$ or $2$ edges

Vishesh Jain, Haoran Luo, Dhruv Mubayi

In 1984, Frankl and FÃ¼redi asked for the maximum density of an $n$ -vertex $r$ -graph in which every $(r + 1)$ -set of vertices spans $0$ or $2$ edges. They gave a construction with as…

math.CO2026

A Jump in the Codegree TurÃ¡n Densities of Long Tight Cycles

JÃ³zsef Balogh, Haoran Luo, Maya Sankar

We study the codegree TurÃ¡n density of $C_{ℓ}^{r}$ , the $r$ -uniform hypergraph tight cycle of length $ℓ$ . A result of Han, Lo, and Sanhueza-Matamala states that if $\e…

math.CO2026

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces

JÃ³zsef Balogh, Haoran Luo

Let $I^\pm (F_{q}^{d}, p)$ be the maximum possible size of a point set in general position in the $p$ -random subset of $F_{q}^{d}$ . In this note, we determine the order of m…

math.CO2025

Multicolor ErdÅs--Rogers Functions

Hong Liu, Haoran Luo, Minghui Ouyang

In this paper, we study a multicolor variant of ErdÅs--Rogers functions. Let $f_{I^\pm_{s}; K_{i_{1}}, \dots, K_{i_{t}}} (n)$ be the largest integer $m$ such that there is always an induce…

On the minimum size of maximal k-wise intersecting families

Local maximum of inducibility profiles

On the maximum density of r-graphs in which every (r+1)-set spans 0 or 2 edges

A Jump in the Codegree TurÃ¡n Densities of Long Tight Cycles

Maximum number of points in general position in a random subset of finite 3-dimensional spaces

Multicolor ErdÅs--Rogers Functions

On the minimum size of maximal $k$ -wise intersecting families

On the maximum density of $r$ -graphs in which every $(r + 1)$ -set spans $0$ or $2$ edges

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces

Multicolor ErdÅs--Rogers Functions