Haoran Luo

activity

20202026

most citedOn the number of forests and connected spanning subgraphs

2 citations · 4 across the 16 of their papers we have counts for

collaborators

16 papers

math.CO2026

The number of sum-free subsets of lattice cubes

Haoran Luo

A subset of the $d$ -dimensional lattice cube $[n]^{d}$ is sum-free if it contains no solution to the equation $x + y = z$ . We study the total number of such subsets. For $d = 1$ , Cameron a…

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

József Balogh, Bernard Lidický, 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 Füredi 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 asy…

math.CO2026

A Jump in the Codegree Turán Densities of Long Tight Cycles

József Balogh, Haoran Luo, Maya Sankar

We study the codegree Turán 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 $\el…

math.CO2025

Multicolor Erdős--Rogers Functions

Hong Liu, Haoran Luo, Minghui Ouyang

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

math.CO2025

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

József Balogh, Haoran Luo

Let $α (F_{q}^{d}, p)$ 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 ma…

math.CO2024

On the thresholds of degenerate hypergraphs

Yu Chen, Jie Han, Haoran Luo

An $n$ -vertex $k$ -uniform hypergraph $G$ is $(d, α)$ -degenerate if $m_{1} (G) \leq d$ and there exists a constant $ε > 0$ such that for every subset $U \subseteq V (G)$ with siz…

math.CO2024

On the maximum $F$ -free induced subgraphs in $K_{t}$ -free graphs

József Balogh, Ce Chen, Haoran Luo

For graphs $F$ and $H$ , let $f_{F, H} (n)$ be the minimum possible size of a maximum $F$ -free induced subgraph in an $n$ -vertex $H$ -free graph. This notion generalizes the Ramsey fun…

math.CO2024

On the maximum number of $r$ -cliques in graphs free of complete $r$ -partite subgraphs

József Balogh, Suyun Jiang, Haoran Luo

We estimate the maximum possible number of cliques of size $r$ in an $n$ -vertex graph free of a fixed complete $r$ -partite graph $K_{s_{1}, s_{2}, \dots, s_{r}}$ . By viewing every $r$ -c…

math.CO2023★ 1 cited

Turán density of long tight cycle minus one hyperedge

József Balogh, Haoran Luo

Denote by $C_{ℓ}^{-}$ the $3$ -uniform hypergraph obtained by removing one hyperedge from the tight cycle on $ℓ$ vertices. It is conjectured that the Turán density of…

math.CO2022★ 1 cited

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

József Balogh, Felix Christian Clemen, Haoran Luo

For every integer $t \geq 0$ , denote by $F_{5}^{t}$ the hypergraph on vertex set ${1, 2, \dots, 5 + t}$ with hyperedges ${123, 124} \cup {34 k : 5 \leq k \leq 5 + t}$ . We determine $\mathr…

math.CO2022

Maximal 3-wise Intersecting Families with Minimum Size: the Odd Case

József Balogh, Ce Chen, Haoran Luo

A family $F$ on ground set ${1, 2, \dots, n}$ is maximal $k$ -wise intersecting if every collection of $k$ sets in $F$ has non-empty intersection, and no other…

math.CO2022

On the Maximum $F_{5}$ -free Subhypergraphs of a Random Hypergraph

Igor Araujo, József Balogh, Haoran Luo

Denote by $F_{5}$ the $3$ -uniform hypergraph on vertex set ${1, 2, 3, 4, 5}$ with hyperedges ${123, 124, 345}$ . Balogh, Butterfield, Hu, and Lenz proved that if $p > K lo g n / n$ for…

math.CO2021

Sharp threshold for the Erdős-Ko-Rado theorem

József Balogh, Robert A. Krueger, Haoran Luo

For positive integers $n$ and $k$ with $n \geq 2 k + 1$ , the Kneser graph $K (n, k)$ is the graph with vertex set consisting of all $k$ -sets of ${1, \dots, n}$ , where two $k$ -sets are ad…

math.CO2020★ 2 cited

On the number of forests and connected spanning subgraphs

Márton Borbényi, Péter Csikvári, Haoran Luo

Let $F (G)$ be the number of forests of a graph $G$ . Similarly let $C (G)$ be the number of connected spanning subgraphs of a connected graph $G$ . We bound $F (G)$ and $C (G)$ for regu…

The number of sum-free subsets of lattice cubes

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 Turán Densities of Long Tight Cycles

Multicolor Erdős--Rogers Functions

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

On the thresholds of degenerate hypergraphs

On the maximum F-free induced subgraphs in Kt​-free graphs

On the maximum number of r-cliques in graphs free of complete r-partite subgraphs

Turán density of long tight cycle minus one hyperedge

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

Maximal 3-wise Intersecting Families with Minimum Size: the Odd Case

On the Maximum F5​-free Subhypergraphs of a Random Hypergraph

Sharp threshold for the Erdős-Ko-Rado theorem

On the number of forests and connected spanning subgraphs

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

On the maximum $F$ -free induced subgraphs in $K_{t}$ -free graphs

On the maximum number of $r$ -cliques in graphs free of complete $r$ -partite subgraphs

On the Maximum $F_{5}$ -free Subhypergraphs of a Random Hypergraph