Zixiang Xu

activity

20182026

most citedSome tight lower bounds for Turán problems via constructions of multi-hypergraphs

6 citations · 15 across the 32 of their papers we have counts for

collaborators

Showing math.COShow all

28 papers · 1 filter

math.CO2026

The homomorphism threshold of odd cycle $C_{2 k - 1}$ is below $\frac{1}{2 k - 1}$

Jian Wang, Shipeng Wang, Zixiang Xu

The homomorphism threshold $δ_{hom} (H)$ of a graph $H$ asks how large the minimum degree of an $H$ -free graph has to be in order to force a homomorphism to a bounded $H$ -fre…

math.CO2026

Economical lattice coverings by determined segments

Gennian Ge, Yang Shu, Zixiang Xu

For fixed $d \geq 2$ , let $τ_{d} (n)$ be the minimum size of a set $S \subseteq {0, \dots, n}^{d}$ such that the affine lines determined by pairs of distinct points of $S$ cover the grid.…

math.CO2026

Largest Sperner families with restricted differences

Gennian Ge, Zixiang Xu, Xiaochen Zhao

Let $L$ be a fixed set of positive integers. A family $F \subseteq 2^{[n]}$ is called $L$ -differencing if $∣ A ∖ B ∣ \in L$ for every ordered pair of distin…

math.CO2026

All simplices exhibit canonical Ramsey property

Gennian Ge, Yang Shu, Zixiang Xu +1

We prove that all nondegenerate simplices have the canonical Ramsey property, thereby resolving a central open problem in canonical Euclidean Ramsey theory and providing a canonica…

math.CO2026

Tverberg's theorem for unions of convex sets: Sharp bounds and colored extensions

Gennian Ge, Yang Shu, Zixiang Xu

Let $f_{r} (d, s_{1}, \dots, s_{r})$ be the least $N$ such that every $N$ -point set $P \subseteq R^{d}$ has an $r$ -partition $P = P_{1} ⊔ \dots ⊔ P_{r}$ with the followin…

math.CO2026

Improvement on the Erdős-Kleitman conjecture via the KKL theorem

Gennian Ge, Jialuo Wang, Zixiang Xu

In 1974, Erdős and Kleitman conjectured that if a family $F \subseteq 2^{[n]}$ contains no matching of size $s$ and is maximal with respect to this property, then $ |\ma…

math.CO2025

A Tverberg-type problem of Kalai: Two negative answers to questions of Alon and Smorodinsky, and the power of disjointness

Wenchong Chen, Gennian Ge, Yang Shu +2

Let $f_{r} (d, s_{1}, \dots, s_{r})$ denote the least integer $n$ such that every $n$ -point set $P \subseteq R^{d}$ admits a partition $P = P_{1} \cup \dots \cup P_{r}$ with the property that…

math.CO2025

Canonical Ramsey: triangles, rectangles and beyond

Yijia Fang, Gennian Ge, Yang Shu +3

In a seminal work, Cheng and Xu showed that if $S$ is a square or a triangle with a certain property, then for every positive integer $r$ there exists $n_{0} (S)$ independent of $r$ s…

math.CO2025

All rectangles exhibit canonical Ramsey property

Gennian Ge, Yang Shu, Zixiang Xu

In a seminal work, Cheng and Xu proved that for any positive integer $r$, there exists an integer $n_0$, independent of $r$, such that every $r$-coloring of the $n$-dimen…

math.CO2024★ 1 cited

The Frankl-Pach upper bound is not tight for any uniformity

Gennian Ge, Zixiang Xu, Chi Hoi Yip +2

For any positive integers $n \geq d + 1 \geq 3$ , what is the maximum size of a $(d + 1)$ -uniform set system in $[n]$ with VC-dimension at most $d$ ? In 1984, Frankl and Pach initiated the s…

math.CO2024

Algebraic approach to stability results for Erdős-Ko-Rado theorem

Gennian Ge, Zixiang Xu, Xiaochen Zhao

Celebrated results often unfold like episodes in a long-running series. In the field of extremal set thoery, Erdős, Ko, and Rado in 1961 established that any $k$ -uniform intersecti…

math.CO2023

A new variant of the Erdős-Gyárfás problem on $K_{5}$

Gennian Ge, Zixiang Xu, Yixuan Zhang

Motivated by an extremal problem on graph-codes that links coding theory and graph theory, Alon recently proposed a question aiming to find the smallest number $t$ such that there…

math.CO2023★ 1 cited

Euclidean Gallai-Ramsey for various configurations

Xinbu Cheng, Zixiang Xu

The Euclidean Gallai-Ramsey problem, which investigates the existence of monochromatic or rainbow configurations in a colored $n$ -dimensional Euclidean space $E^{n}$ , was…

math.CO2023

Extremal number of graphs from geometric shapes

Jun Gao, Oliver Janzer, Hong Liu +1

We study the Turán problem for highly symmetric bipartite graphs arising from geometric shapes and periodic tilings commonly found in nature. 1. The prism $C_{2\ell}^{\square}:=C_{…

math.CO2023★ 1 cited

Exact values and improved bounds on $k$ -neighborly families of boxes

Xinbu Cheng, Meiqin Wang, Zixiang Xu +1

A finite family $F$ of $d$ -dimensional convex polytopes is called $k$ -neighborly if $d - k \leq dim (C \cap C^{'}) \leq d - 1$ for any two distinct members $C,C'\in\mathcal{F}…

math.CO2022

Stability through non-shadows

Jun Gao, Hong Liu, Zixiang Xu

We study families $F \subseteq 2^{[n]}$ with restricted intersections and prove a conjecture of Snevily in a stronger form for large $n$ . We also obtain stability results…

math.CO2022★ 1 cited

Sperner systems with restricted differences

Zixiang Xu, Chi Hoi Yip

Let $F$ be a family of subsets of $[n]$ and $L$ be a subset of $[n]$ . We say $F$ is an $L$ -differencing Sperner system if $∣ A ∖ B ∣ \in L$ for any distinct…

math.CO2022

Local rainbow colorings for various graphs

Xinbu Cheng, Zixiang Xu

Motivated by a problem in theoretical computer science suggested by Wigderson, Alon and Ben-Eliezer studied the following extremal problem systematically one decade ago. Given a gr…

math.CO2022

Intersective sets over abelian groups

Zixiang Xu, Chi Hoi Yip

Given a finite abelian group $G$ and a subset $J \subset G$ with $0 \in J$ , let $D_{G} (J, N)$ be the maximum size of $A \subset G^{N}$ such that the difference set $A - A$ and $J^{N}$ ha…

math.CO2021

A note on multicolor Ramsey number of small odd cycles versus a large clique

Zixiang Xu, Gennian Ge

Let $R_{k} (H; K_{m})$ be the smallest number $N$ such that every coloring of the edges of $K_{N}$ with $k + 1$ colors has either a monochromatic $H$ in color $i$ for some $1\leqslant i\le…

math.CO2021★ 1 cited

A polynomial resultant approach to algebraic constructions of extremal graphs

Tao Zhang, Zixiang Xu, Gennian Ge

The Turán problem asks for the largest number of edges ex $(n, H)$ in an $n$ -vertex graph not containing a fixed forbidden subgraph $H$ , which is one of the most important problems i…

math.CO2020★ 1 cited

On color isomorphic subdivisions

Zixiang Xu, Gennian Ge

Given a graph $H$ and an integer $k ⩾ 2$ , let $f_{k} (n, H)$ be the smallest number of colors $C$ such that there exists a proper edge-coloring of the complete graph $K_{n}$ w…

math.CO2020

Color isomorphic even cycles and a related Ramsey problem

Zixiang Xu, Tao Zhang, Yifan Jing +1

In this paper, we first study a new extremal problem recently posed by Conlon and Tyomkyn~(arXiv: 2002.00921). Given a graph $H$ and an integer $k ⩾ 2$ , let $f_{k} (n, H)$ be…

math.CO2020

On the Turán number of 1-subdivision of $K_{3, t}$

Tao Zhang, Zixiang Xu, Gennian Ge

For a graph $H$ , the 1-subdivision of $H$ , denoted by $H^{'}$ , is the graph obtained by replacing the edges of $H$ by internally disjoint paths of length 2. Recently, Conlon, Janzer a…

The homomorphism threshold of odd cycle C2k−1​ is below 2k−11​

Economical lattice coverings by determined segments

Largest Sperner families with restricted differences

All simplices exhibit canonical Ramsey property

Tverberg's theorem for unions of convex sets: Sharp bounds and colored extensions

Improvement on the Erdős-Kleitman conjecture via the KKL theorem

A Tverberg-type problem of Kalai: Two negative answers to questions of Alon and Smorodinsky, and the power of disjointness

Canonical Ramsey: triangles, rectangles and beyond

All rectangles exhibit canonical Ramsey property

The Frankl-Pach upper bound is not tight for any uniformity

Algebraic approach to stability results for Erdős-Ko-Rado theorem

A new variant of the Erdős-Gyárfás problem on K5​

Euclidean Gallai-Ramsey for various configurations

Extremal number of graphs from geometric shapes

Exact values and improved bounds on k-neighborly families of boxes

Stability through non-shadows

Sperner systems with restricted differences

Local rainbow colorings for various graphs

Intersective sets over abelian groups

A note on multicolor Ramsey number of small odd cycles versus a large clique

A polynomial resultant approach to algebraic constructions of extremal graphs

On color isomorphic subdivisions

Color isomorphic even cycles and a related Ramsey problem

On the Turán number of 1-subdivision of K3,t​

The homomorphism threshold of odd cycle $C_{2 k - 1}$ is below $\frac{1}{2 k - 1}$

A new variant of the Erdős-Gyárfás problem on $K_{5}$

Exact values and improved bounds on $k$ -neighborly families of boxes

On the Turán number of 1-subdivision of $K_{3, t}$