Haixiang Zhang

collaborators

16 papers

math.CO2026

A Near-Optimal Linear Range for the Erdős Matching Conjecture

Mengyu Cao, Hong Liu, Haixiang Zhang

The Erdős Matching Conjecture is governed by two competing ways of excluding $s + 1$ disjoint edges: one may concentrate all edges on fewer than $k (s + 1)$ vertices, or force every edg…

math.CO2026

Extremal Families for Matchings in Permutations

Mengyu Cao, Haixiang Zhang

Two permutations $σ, τ \in S_{n}$ are called disjoint if the composition $σ τ^{- 1}$ has no fixed point. If a family $F \subseteq S_{n}$ contains no $s$ pairwise disjoint permutati…

math.CO2026

A Sharp Spectral Erdős--Ko--Rado Theorem for Uniform Hypergraphs

Mengyu Cao, Mei Lu, Haixiang Zhang

The spectral Erdős--Ko--Rado problem asks for the largest adjacency-tensor spectral radius of a $t$ -intersecting $k$ -uniform family. Keevash, Lenz and Mubayi proved that, for fixed…

math.CO2026

Entropy Transference for Rainbow- $H$ -Free Colourings of Random Graphs

Mengyu Cao, Mei Lu, Haixiang Zhang

Let $H$ be a fixed graph with $e (H) \geq 3$ that contains two adjacent edges, and let $ℓ \geq e (H)$ be fixed. We establish an entropy-transference principle for rainbow- $H$ -free edge…

math.CO2026

Erdős--Ko--Rado and Hilton--Milner Theorems in the Partition Lattice

Mengyu Cao, Jiaqi Liao, Haixiang Zhang

Let $M_{n} = M (K_{n + 1})$ be the graphic matroid of the complete graph, and let $F_{k} (M_{n})$ be its rank- $k$ flats. We study families $A \subseteq F_{k} (M_{n})$ sa…

math.CO2026

Degree Power Sums in Extremal Set Systems

Mengyu Cao, Mei Lu, Haixiang Zhang

For a family $F \subseteq (k [ n ])$ and $R \in (r [ n ])$ , let $d_{F} (R) = ∣ {F \in F : R \subseteq F} ∣$ and $\ell_{r,p}(\mathcal F)=\sum_{R\in\binom{[n]}r}…

math.CO2026

Projective Ore-Degree Conditions for Intersection Theorems in Vector Spaces

Mengyu Cao, Mei Lu, Xuyang Yan +1

Let $V$ be an $n$ -dimensional vector space over the finite field $F_{q}$ , and let $F ⊊ [k V]$ . The \emph{projective Ore-degree} of $\mat…

math.CO2026

Algorithm for finding vertex-edge domination number on graphs with bounded treewidth and related problems on planar graphs

Yichen Wang, Haixiang Zhang, Mei Lu

Given a graph $G = (V, E)$ , a vertex $u \in V$ {\em ve-dominates} all edges incident to any vertex of $N_{G} [u]$ . A set $S \subseteq V$ is a {\em ve-dominating set} if for all edges $e\…

math.CO2026

On degree bounds of $k$ -uniform hypergraphs with bounded matching number

Haixiang Zhang, Mengyu Cao, Mei Lu

We study the connection between the degree sequence of a $k$ -uniform hypergraph and the size of its largest matching. Let $F$ be a $k$ -uniform hypergraph on $n$ vertices…

math.CO2026

Counting sunflowers with restricted matching number

Haixiang Zhang, Mengyu Cao, Mei Lu

For $H \subseteq (k [ n ])$ , let $ν (H)$ denote its matching number and let $d_{H} (E)$ denote the codegree of a $(k - 1)$ -set $E$ . We study the codegree mo…

math.CO2025

The maximum sum of sizes of non-empty cross $L$ -intersecting families

Xiamiao Zhao, Haixiang Zhang, Mei Lu

Let $n$ , $r$ , and $k$ be positive integers such that $k, r \geq 2$ , $L$ a non-empty subset of $[k]$ , and $F_{i} \subseteq (k [ n ])$ for $1 \leq i \leq r$ . We say that…

math.CO2025

Cross-intersection theorems for uniform partitions of finite sets

Tian Yao, Mengyu Cao, Haixiang Zhang

A set partition is $c$ -uniform if every block has size $c$ . Two families of $c$ -uniform partitions of a finite set are said to be cross $t$ -intersecting if two partitions from diff…

math.CO2025

Counting induced subgraphs with given intersection sizes

Haixiang Zhang, Yichen Wang, Xiamiao Zhao +1

Let $F$ be a graph of order $r$ . In this paper, we study the maximum number of induced copies of $F$ with restricted intersections, which highlights the motivation from extremal se…

math.CO2025

Generalizations of the Erdős Matching Conjecture for the $t$ -Matching Number

Mengyu Cao, Mei Lu, Haixiang Zhang

We write finite set systems as uniform hypergraphs. A \emph{ $t$ -matching} in a $k$ -uniform hypergraph is a set of hyperedges any two of which intersect in fewer than $t$ vertices.…

math.CO2025

Turán type problems for a fixed graph and a linear forest

Haixiang Zhang, Xiamiao Zhao, Mei Lu

Let $F$ be a family of graphs. A graph $G$ is $F$ -free if $G$ does not contain any $F \in F$ as a subgraph. The Turán number, denoted by $ex(n, \mathsc…

math.CO2025

Simplices in $t$ -intersecting families for vector spaces

Haixiang zhang, Mengyu Cao, Mei Lu +1

Let $V$ be an $n$ -dimensional vector space over the finite field $F_{q}$ and $[k V]$ denote the family of all $k$ -dimensional subspaces of $V$ . A family $\mathcal{F}\s…

A Near-Optimal Linear Range for the Erdős Matching Conjecture

Extremal Families for Matchings in Permutations

A Sharp Spectral Erdős--Ko--Rado Theorem for Uniform Hypergraphs

Entropy Transference for Rainbow-H-Free Colourings of Random Graphs

Erdős--Ko--Rado and Hilton--Milner Theorems in the Partition Lattice

Degree Power Sums in Extremal Set Systems

Projective Ore-Degree Conditions for Intersection Theorems in Vector Spaces

Algorithm for finding vertex-edge domination number on graphs with bounded treewidth and related problems on planar graphs

On degree bounds of k-uniform hypergraphs with bounded matching number

Counting sunflowers with restricted matching number

The maximum sum of sizes of non-empty cross L-intersecting families

Cross-intersection theorems for uniform partitions of finite sets

Counting induced subgraphs with given intersection sizes

Generalizations of the Erdős Matching Conjecture for the t-Matching Number

Turán type problems for a fixed graph and a linear forest

Simplices in t-intersecting families for vector spaces

Entropy Transference for Rainbow- $H$ -Free Colourings of Random Graphs

On degree bounds of $k$ -uniform hypergraphs with bounded matching number

The maximum sum of sizes of non-empty cross $L$ -intersecting families

Generalizations of the Erdős Matching Conjecture for the $t$ -Matching Number

Simplices in $t$ -intersecting families for vector spaces