Xizhi Liu

activity

20182026

most citedA unified approach to hypergraph stability

16 citations · 57 across the 76 of their papers we have counts for

collaborators

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75 papers · 1 filter

math.CO2026

Improved Sidorenko bound for hypergraph Turan densities

Shuyan Chen, Xinmin Hou, Xizhi Liu

For every fixed integer $r \geq 3$ , we prove that the Turán density of every $r$ -uniform hypergraph $F$ with $m \geq 1$ edges satisfies $π (F) \leq 1 - c_{r} m^{- (r - 1) / r}$ , where $c_{r} > 0$ depends…

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.CO2026

Tight Hamiltonian Cycles in Uniformly Dense $3$ -Graphs

Yaobin Chen, Jie Han, Xizhi Liu

We study minimum degree conditions for tight Hamiltonian cycles in uniformly dense $3$ -uniform hypergraphs. We prove that for every $d, α > 0$ , every sufficiently large $(ρ, d)$ -dense…

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

The inducibility of 6-vertex graphs

Levente Bodnár, Jun Gao, Jared León +3

The inducibility constant $λ_{F}$ of a graph $F$ is the asymptotically maximum induced density of $F$ in a growing sequence of graphs. This paper systematically investigates the ca…

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

Turán numbers of $4$ -uniform tight even cycles minus one edge

Wanfang Chen, Jianfeng Hou, Xizhi Liu +2

For every integer $k \geq 1$ and sufficiently large $n$ , we show that the extremal construction for the Turán number of the $4$ -uniform tight cycle of length $4 k + 2$ minus one edge i…

math.CO2026

Exact extremal constructions for the inducibility of blowup graphs

Wanfang Chen, Xizhi Liu

For a finite graph $H$ and a positive integer $h$ , the $h$ -blowup $H^{(h)}$ of $H$ is the graph obtained by replacing each vertex of $H$ by a set of size $h$ and each edge by a com…

math.CO2026

Vertex-colored Turán theorems with applications in extremal hypergraph problems

Wanfang Chen, Jinghua Deng, Jianfeng Hou +2

Balogh, Clemen, and Lidický proved that the $ℓ_{2}$ -norm Turán problem for $K_{5}^{3}$ is asymptotically solved by the balanced bipartite construction, and they further conjectu…

math.CO2026

Upper Bounds on Turán Densities via Extremal Set Theory

Yaobin Chen, Xizhi Liu, Ningyuan Yang +1

We exhibit, in a systematic way, connections between hypergraph Turán problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for…

math.CO2026

The spectral inducibility of graphs

Liying Kang, Xizhi Liu, Yongchun Lu

We introduce a spectral version of the classical inducibility problem. Given an $ℓ$ -vertex graph $F$ and an $n$ -vertex graph $G$ , let $H_{F} (G)$ be the $ℓ$ -uniform hypergraph w…

math.CO2026

The Erdős Matching Conjecture for 4-uniform hypergraphs

Jianfeng Hou, Caiyun Hu, Xizhi Liu

We prove the Erdős Matching Conjecture for $4$ -uniform hypergraphs for every matching number $s \geq 6004$ . Specifically, for integers $s \geq 6004$ and $n \geq 4 s + 4$ , if a $n$ -vertex 4-u…

math.CO2026

Intervals of hypergraph Turán densities

Xizhi Liu, Oleg Pikhurko

We prove that, for every integer $r \geq 3$ , the set $Π_{\infty}^{(r)}$ of Turán densities of (possibly infinite) families of $r$ -graphs contains non-degenerate intervals, including an…

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.CO2026

The spectral radius of $k$ -chromatic $r$ -graphs

Xizhi Liu, Junchi Luo

For an $r$ -uniform hypergraph $G$ , let $λ^{(p)} (G)$ denote its $p$ -spectral radius, defined as the maximum of the polyform of $G$ over the unit sphere in the $ℓ_{p}$ -norm. Let $Q_…

math.CO2026

The number $4/9$ is a non-jump for $3$ -graphs

Xizhi Liu, Dhruv Mubayi

We prove that $4/9$ is a non-jump for $3$ -uniform hypergraphs. Our construction perturbs the $A B B$ pattern by inserting, inside the $B$ -part, the union of a high-cogirth pair of St…

math.CO2026

A note on the $t$ -partite link problem of Füredi

Jianfeng Hou, Xinmin Hou, Xizhi Liu +2

Motivated by the Erdős--Sós bipartite link conjecture, Füredi (Oberwolfach, 2004) asked for the asymptotic maximum edge density $π_{link} (t)$ of $3$ -graphs in which the li…

math.CO2026

The inducibility of Turán graphs

Xizhi Liu, Jie Ma, Tianming Zhu

Let $I (F, n)$ denote the maximum number of induced copies of a graph $F$ in an $n$ -vertex graph. The inducibility of $F$ , defined as $i (F) = lim_{n \to \infty} I (F, n) / (v ( F ) n)$ …

math.CO2025

Andr{á}sfai--Erdős--Sós theorem under max-degree constraints

Xizhi Liu, Sijie Ren, Jian Wang

We establish the following strengthening of the celebrated Andr{á}sfai--Erdős--Sós theorem: If $G$ is an $n$ -vertex $K_{r + 1}$ -free graph whose minimum degree $δ (G)$ and maximum deg…

math.CO2025

Tetrahedron Conjecture in the $ℓ_{2}$ -norm

Levente Bodnár, Wanfang Chen, Jinghua Deng +5

The famous Tetrahedron Conjecture of Turán from the 1940s asserts that the number of edges in an $n$ -vertex $3$ -graph without the tetrahedron, the complete $3$ -graph on four vertic…

math.CO2025

Odd hypergraph Mantel theorems

Jianfeng Hou, Xizhi Liu, Yixiao Zhang +2

A classical result of Sidorenko (1989) shows that the Turán density of every $r$ -uniform hypergraph with three edges is bounded from above by $1/2$ . For even $r$ , this bound is tig…

Improved Sidorenko bound for hypergraph Turan densities

Turing universality, computability, and incompleteness in hypergraph Turán theory

Tight Hamiltonian Cycles in Uniformly Dense 3-Graphs

Forcing Quasirandomness via Rooted F-Densities

Intervals of uniform Turán densities

The inducibility of 6-vertex graphs

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

Turán numbers of 4-uniform tight even cycles minus one edge

Exact extremal constructions for the inducibility of blowup graphs

Vertex-colored Turán theorems with applications in extremal hypergraph problems

Upper Bounds on Turán Densities via Extremal Set Theory

The spectral inducibility of graphs

The Erdős Matching Conjecture for 4-uniform hypergraphs

Intervals of hypergraph Turán densities

A single 3-graph with infinite stability number

The spectral radius of k-chromatic r-graphs

The number 4/9 is a non-jump for 3-graphs

A note on the t-partite link problem of Füredi

The inducibility of Turán graphs

Andr{á}sfai--Erdős--Sós theorem under max-degree constraints

Tetrahedron Conjecture in the ℓ2​-norm

Odd hypergraph Mantel theorems

Tight Hamiltonian Cycles in Uniformly Dense $3$ -Graphs

Turán numbers of $4$ -uniform tight even cycles minus one edge

A single $3$ -graph with infinite stability number

The spectral radius of $k$ -chromatic $r$ -graphs

The number $4/9$ is a non-jump for $3$ -graphs

A note on the $t$ -partite link problem of Füredi

Tetrahedron Conjecture in the $ℓ_{2}$ -norm