Heng Li

I am currently a visiting scholar in the Extremal Combinatorics and Probability Group (ECOPRO) at the Institute for Basic Science (IBS) in South Korea, working with Professor Hong Liu.

From July 2023 to July 2026, I was a postdoctoral researcher at Shandong University, working with Professor Guanghui Wang.

I received my Ph.D. from Fuzhou University in June 2023 under the supervision of Professor Jianfeng Hou.

Publications

Preprints / Submitted

Comments are welcome.

01
Superlinear lower bounds for monochromatic path partitions
Heng Li, Lanchao Wang
arXiv ↗
02
Forcing quasirandomness via rooted F-densities
Heng Li, Xizhi Liu
arXiv ↗
03
Intervals of uniform Turán densities
Heng Li, Xizhi Liu, Oleg Pikhurko
arXiv ↗
04
Nearly sharp bounds for lattice coverings by convex bodies
Heng Li, Xizhi Liu
arXiv ↗
05
A higher-order clique density theorem
Heng Li, Hong Liu, Yixiao Zhang
arXiv ↗
06
Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity
Heng Li, Hong Liu, Xizhi Liu, Jing Wang
arXiv ↗
07
Sharp bounds for minimal dependencies of linear-form powers
Heng Li, Xizhi Liu
arXiv ↗
08
On a hypergraph Turán problem of Balogh–Bohman–Bollobás–Zhao
Heng Li, Jie Ma, Tianhen Wang, Yixiao Zhang, Tianming Zhu
arXiv ↗
09
Physical-space scarring in generic Bunimovich stadia
Heng Li, Xizhi Liu
arXiv ↗
10
On Mubayi's polynomial-ideal conjecture and a hypergraph Turán theorem
Heng Li, Xizhi Liu
arXiv ↗
11
A single 3-graph with infinite stability number
Heng Li, Xizhi Liu
arXiv ↗
12
Hypergraphs with irrational Turán density and many extremal configurations
Jianfeng Hou, Heng Li, Guanghui Wang, Yixiao Zhang
arXiv ↗

Published / Accepted

01
Transversal Hamilton cycles in digraph collections
Yangyang Cheng, Heng Li, Wanting Sun, Guanghui Wang
Combinatorics, Probability and Computing, First View, 1–57 (2026) ↗
arXiv ↗
02
On the boundedness of degenerate hypergraphs
Jianfeng Hou, Caiyun Hu, Heng Li, Xizhi Liu, Caihong Yang, Yixiao Zhang
Acta Mathematica Sinica, English Series 42(2), 464–480 (2026) ↗
arXiv ↗
03
Many vertex-disjoint even cycles of fixed length in a graph
Jianfeng Hou, Caiyun Hu, Heng Li, Xizhi Liu, Caihong Yang, Yixiao Zhang
Journal of Graph Theory 111(3), 67–77 (2026) ↗
arXiv ↗
04
Infinitely many accumulation points of codegree Turán densities
Heng Li, Weichan Liu, Bjarne Schülke, Wanting Sun
Combinatorial Theory, to appear ↗
arXiv ↗
05
Toward a density Corrádi–Hajnal theorem for degenerate hypergraphs
Jianfeng Hou, Caiyun Hu, Heng Li, Xizhi Liu, Caihong Yang, Yixiao Zhang
Journal of Combinatorial Theory, Series B 172, 221–262 (2025) ↗
arXiv ↗
06
A step towards a general density Corrádi–Hajnal theorem
Jianfeng Hou, Heng Li, Xizhi Liu, Long-Tu Yuan, Yixiao Zhang
Canadian Journal of Mathematics, First View, 1–36 (2025) ↗
arXiv ↗
07
Two stability theorems for 𝒦ₗ₊₁ʳ-saturated hypergraphs
Jianfeng Hou, Heng Li, Caihong Yang, Qinghou Zeng, Yixiao Zhang
Journal of Graph Theory 109(4), 492–504 (2025) ↗
arXiv ↗
08
Extremal graphs for the suspension of edge-critical graphs
Jianfeng Hou, Heng Li, Qinghou Zeng
The Electronic Journal of Combinatorics 31(4), #P4.55 (2024) ↗
arXiv ↗
09
A 2-stable family of triple systems
Yixiao Zhang, Jianfeng Hou, Heng Li
The Electronic Journal of Combinatorics 31(2), #P2.3 (2024) ↗
10
A family of 4-uniform hypergraphs with no stability
Yixiao Zhang, Heng Li, Jianfeng Hou
Scientia Sinica Mathematica 54(11), 1905–1924 (2024) ↗
11
Generating non-jumps from a known one
Jianfeng Hou, Heng Li, Caihong Yang, Yixiao Zhang
Science China Mathematics 67(12), 2899–2908 (2024) ↗
arXiv ↗
12
Hypergraphs with infinitely many extremal constructions
Jianfeng Hou, Heng Li, Xizhi Liu, Dhruv Mubayi, Yixiao Zhang
Discrete Analysis 2023:18 (2023) ↗
arXiv ↗
13
Singular Turán numbers of stars
Gaoxing Sun, Heng Li, Qinghou Zeng, Jianfeng Hou
Pure and Applied Mathematics Quarterly 18(6), 2599–2618 (2022) ↗
14
On (3, r)-choosability of some planar graphs
Heng Li, Jianfeng Hou, Hongguo Zhu
Bulletin of the Malaysian Mathematical Sciences Society 45(2), 851–867 (2022) ↗

Research Notes

01
On the spectrum of minimum ℓ-degree Turán densities
Heng Li, Xizhi Liu
Manuscript ↗
02
Turing universality, computability, and incompleteness in hypergraph Turán theory
Heng Li, Xizhi Liu
Manuscript ↗
03
A finite family with transcendental uniform Turán density
Heng Li, Xizhi Liu
Manuscript ↗
04
Undecidability in uniform Turán densities
Heng Li, Xizhi Liu
Manuscript ↗
05
Gaps between Turán densities for r-graphs on r + 1 vertices
Heng Li, Xizhi Liu
Manuscript ↗
06
On the VC-dimension of Erdős–Rényi random graphs
Xizhi Liu, Heng Li
Manuscript ↗
07
Transcendence and undecidability for ℓ-degree Turán densities
Heng Li, Xizhi Liu
Manuscript ↗
08
Transcendence and undecidability in hypergraph Turán densities
Heng Li, Hong Liu, Xizhi Liu
Manuscript ↗
09
The anti-supersaturation problem
Heng Li, Xizhi Liu, Jiasheng Zeng
Manuscript ↗
10
A note on Bukh's construction of extremal graphs without small bicliques
Heng Li, Xizhi Liu
Manuscript ↗
11
Logarithmic colourings, monomial shrinking targets, and product-configuration obstructions
Heng Li, Xizhi Liu
Manuscript ↗

Heng Li

Publications

Preprints / Submitted

Superlinear lower bounds for monochromatic path partitions

Forcing quasirandomness via rooted F-densities

Intervals of uniform Turán densities

Nearly sharp bounds for lattice coverings by convex bodies

A higher-order clique density theorem

Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity

Sharp bounds for minimal dependencies of linear-form powers

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

Physical-space scarring in generic Bunimovich stadia

On Mubayi's polynomial-ideal conjecture and a hypergraph Turán theorem

A single 3-graph with infinite stability number

Hypergraphs with irrational Turán density and many extremal configurations

Published / Accepted

Transversal Hamilton cycles in digraph collections

On the boundedness of degenerate hypergraphs

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

Infinitely many accumulation points of codegree Turán densities

Toward a density Corrádi–Hajnal theorem for degenerate hypergraphs

A step towards a general density Corrádi–Hajnal theorem

Two stability theorems for 𝒦ₗ₊₁ʳ-saturated hypergraphs

Extremal graphs for the suspension of edge-critical graphs

A 2-stable family of triple systems

A family of 4-uniform hypergraphs with no stability

Generating non-jumps from a known one

Hypergraphs with infinitely many extremal constructions

Singular Turán numbers of stars

On (3, r)-choosability of some planar graphs

Research Notes

On the spectrum of minimum ℓ-degree Turán densities

Turing universality, computability, and incompleteness in hypergraph Turán theory

A finite family with transcendental uniform Turán density

Undecidability in uniform Turán densities

Gaps between Turán densities for r-graphs on r + 1 vertices

On the VC-dimension of Erdős–Rényi random graphs

Transcendence and undecidability for ℓ-degree Turán densities

Transcendence and undecidability in hypergraph Turán densities

The anti-supersaturation problem

A note on Bukh's construction of extremal graphs without small bicliques

Logarithmic colourings, monomial shrinking targets, and product-configuration obstructions