Heng Li

activity

20222026

most citedHypergraphs with infinitely many extremal constructions

7 citations · 10 across the 20 of their papers we have counts for

collaborators

21 papers

math.CO2026

Colored Turán densities and finite directed templates

Nannan Chen, Ander Lamaison, Heng Li +1

Classical Turán theory relates the asymptotic extremal problem for an ordinary forbidden graph to its chromatic number. This principle fails when a forbidden copy must respect pres…

math.CO2026

Turing universality, computability, and incompleteness in hypergraph Turán theory

Heng Li, Xizhi Liu

Given a finite family $F$ of forbidden $r$ -graphs, the Turán problem asks for the maximum asymptotic edge density of $F$ -free $r$ -graphs and the structure of near…

math.MG2026

Nearly Sharp Bounds for Lattice Coverings by Convex Bodies

Heng Li, Xizhi Liu

For an $n$ -dimensional convex body $K$ , let $θ_{L} (K)$ denote its lattice covering density, and let $Θ_{L}^{conv} (n)$ and $Θ_{L}^{sym} (n)$ be the corresponding worst-ca…

math.CO2026

Forcing Quasirandomness via Rooted F-Densities

Heng Li, Xizhi Liu

Let $F$ be a finite graph with at least one edge, and let $W$ be a graphon. We show that if the density of $F$ rooted at each edge is almost everywhere constant, then either $t(F,W…

math.CO2026

Intervals of uniform Turán densities

Heng Li, Xizhi Liu, Oleg Pikhurko

We prove that the set $Π_{∴, \infty}$ of uniform Turán densities of possibly infinite families of $3$ -graphs contains a terminal interval: there exists $δ > 0$ such that $[1-…

math.CO2026

A Higher-Order Clique Density Theorem

Heng Li, Hong Liu, Yixiao Zhang

Reiher's clique density theorem determines the sharp lower envelope for the density of $K_{r}$ at fixed edge density. We prove a higher-order version in which the prescribed quantity…

math.CO2026

Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity

Heng Li, Hong Liu, Xizhi Liu +1

The supersaturation problem asks, for a fixed $r$ -graph $F$ , for the minimum number of copies of $F$ in an $n$ -vertex $r$ -graph with $\ex(n,\mathcal F)+q$ edges.…

math.CO2026

On Mubayi's Polynomial-Ideal Conjecture and a Hypergraph Turán Theorem

Heng Li, Xizhi Liu

Among the many proofs of Turán's classical theorem, one particularly surprising proof due to Li and Li uses ideals in polynomial rings to record missing edges. Motivated by their p…

math.CO2026

Sharp bounds for minimal dependencies of linear-form powers

Heng Li, Xizhi Liu

Motivated by the dimension-bound part of a problem of Bukh, we study Veronese circuits: how large can the span of $t$ linear forms be if their $m$ -th powers are minimally linearly…

math.CO2026

On a hypergraph Turán problem of Balogh-Bohman-Bollobás-Zhao

Heng Li, Jie Ma, Tianhen Wang +2

Let $S$ and $T$ be disjoint sets with $∣ S ∣ = i$ and $∣ T ∣ = r - 1$ for $2 \leq i \leq r - 1$ , and let $B_{i}^{(r)}$ be the $r$ -graph on $S \cup T$ whose edges are the $r$ -subsets containing $S$ or…

math.CO2026

From Halin's Edge Removability to Matching Removability in $k$ -Connected Graphs

Hengzhe Li, Mingming Zhou, Shinya Fujita +1

We study matching-removability under the degree/connectivity regime of Halin's theorem, which asserts that every $k$ -connected graph $G$ with minimum degree $δ (G) \geq k + 1$ contains…

math.CO2026

A single $3$ -graph with infinite stability number

Heng Li, Xizhi Liu

The stability number of a forbidden family measures how many different structures are needed to approximate all near-extremal constructions avoiding it. An infinite stability numbe…

math.CO2024★ 1 cited

On the boundedness of degenerate hypergraphs

Jianfeng Hou, Caiyun Hu, Heng Li +3

We investigate the impact of a high-degree vertex in Turán problems for degenerate hypergraphs (including graphs). We say an $r$ -graph $F$ is bounded if there exist constants $α, β…

math.CO2023

Many vertex-disjoint even cycles of fixed length in a graph

Jianfeng Hou, Caiyun Hu, Heng Li +3

For every integer $k \geq 3$ , we determine the extremal structure of an $n$ -vertex graph with at most $t$ vertex-disjoint copies of $C_{2 k}$ when $n$ is sufficiently large and $t$ l…

math.CO2023★ 1 cited

Toward a density Corrádi--Hajnal theorem for degenerate hypergraphs

Jianfeng Hou, Caiyun Hu, Heng Li +3

Given an $r$ -graph $F$ with $r \geq 2$ , let $ex (n, (t + 1) F)$ denote the maximum number of edges in an $n$ -vertex $r$ -graph with at most $t$ pairwise vertex-disjoint copies…

math.CO2023

Hypergraphs with irrational Turán density and many extremal configurations

Jianfeng Hou, Heng Li, Guanghui Wang +1

Unlike graphs, determining Turán densities of hypergraphs is known to be notoriously hard in general. The essential reason is that for many classical families of $r$ -uniform hyperg…

math.CO2023★ 1 cited

A step towards a general density Corrádi--Hajnal Theorem

Jianfeng Hou, Heng Li, Xizhi Liu +2

For a nondegenerate $r$ -graph $F$ , large $n$ , and $t$ in the regime $[0, c_{F} n]$ , where $c_{F} > 0$ is a constant depending only on $F$ , we present a general approach for determining…

math.CO2022

Extremal graphs for the suspension of edge-critical graphs

Jianfeng Hou, Heng Li, Qinghou Zeng

The Turán number of a graph $H$ , $ex (n, H)$ , is the maximum number of edges in an $n$ -vertex graph that does not contain $H$ as a subgraph. For a vertex $v$ and a multi-set $…

math.CO2022

Two stability theorems for $K_{ℓ + 1}^{r}$ -saturated hypergraphs

Jianfeng Hou, Heng Li, Caihong Yang +2

An $F$ -saturated $r$ -graph is a maximal $r$ -graph not containing any member of $F$ as a subgraph. Let $K_{ℓ + 1}^{r}$ be the collection of all $r$ -…

math.CO2022

Generating non-jumps from a known one

Jianfeng Hou, Heng Li, Caihong Yang +1

Let $r \geq 2$ be an integer. The real number $α \in [0, 1]$ is a jump for $r$ if there exists a constant $c > 0$ such that for any $ε > 0$ and any integer $m \geq r$ , there exists an in…

math.CO2022★ 7 cited

Hypergraphs with infinitely many extremal constructions

Jianfeng Hou, Heng Li, Xizhi Liu +2

We give the first exact and stability results for a hypergraph Turán problem with infinitely many extremal constructions that are far from each other in edit-distance. This include…

Colored Turán densities and finite directed templates

Turing universality, computability, and incompleteness in hypergraph Turán theory

Nearly Sharp Bounds for Lattice Coverings by Convex Bodies

Forcing Quasirandomness via Rooted F-Densities

Intervals of uniform Turán densities

A Higher-Order Clique Density Theorem

Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity

On Mubayi's Polynomial-Ideal Conjecture and a Hypergraph Turán Theorem

Sharp bounds for minimal dependencies of linear-form powers

On a hypergraph Turán problem of Balogh-Bohman-Bollobás-Zhao

From Halin's Edge Removability to Matching Removability in k-Connected Graphs

A single 3-graph with infinite stability number

On the boundedness of degenerate hypergraphs

Many vertex-disjoint even cycles of fixed length in a graph

Toward a density Corrádi--Hajnal theorem for degenerate hypergraphs

Hypergraphs with irrational Turán density and many extremal configurations

A step towards a general density Corrádi--Hajnal Theorem

Extremal graphs for the suspension of edge-critical graphs

Two stability theorems for Kℓ+1r​-saturated hypergraphs

Generating non-jumps from a known one

Hypergraphs with infinitely many extremal constructions

From Halin's Edge Removability to Matching Removability in $k$ -Connected Graphs

A single $3$ -graph with infinite stability number

Two stability theorems for $K_{ℓ + 1}^{r}$ -saturated hypergraphs