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

33 papers

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…

cs.IT2025

Private Information Retrieval over Graphs

Gennian Ge, Hao Wang, Zixiang Xu +1

The problem of PIR in graph-based replication systems has received significant attention in recent years. A systematic study was conducted by Sadeh, Gu, and Tamo, where each file i…

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…

cs.IT2025

Optimal Reconstruction Codes with Given Reads in Multiple Burst-Substitutions Channels

Wenjun Yu, Yubo Sun, Zixiang Xu +2

We study optimal reconstruction codes over the multiple-burst substitution channel. Our main contribution is establishing a trade-off between the error-correction capability of the…

cs.IT2025

Optimal redundancy of function-correcting codes

Gennian Ge, Zixiang Xu, Xiande Zhang +1

Function-correcting codes, introduced by Lenz, Bitar, Wachter-Zeh, and Yaakobi, protect specific function values of a message rather than the entire message. A central challenge is…

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…

cs.IT2022

A generic framework for coded caching and distributed computation schemes

Min Xu, Zixiang Xu, Gennian Ge +1

Several network communication problems are highly related such as coded caching and distributed computation. The centralized coded caching focuses on reducing the network burden in…

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…

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

Private Information Retrieval over Graphs

All rectangles exhibit canonical Ramsey property

Optimal Reconstruction Codes with Given Reads in Multiple Burst-Substitutions Channels

Optimal redundancy of function-correcting codes

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

A generic framework for coded caching and distributed computation schemes

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

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