Mei Lu

collaborators

10 papers

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

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

Matchings and Near-Optimal 2-Factor Packings in Percolated Vertex-Transitive Graphs

Mengyu Cao, Mei Lu, Xiamiao Zhao

Let $G$ be a connected simple vertex-transitive graph on $n$ vertices with degree $d$ , and let $G_{p}$ be the random spanning subgraph obtained by retaining each edge of $G$ independ…

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

Edge pancyclic Cayley graphs on symmetric group

Mengyu Cao, Mei Lu, Zequn Lv +1

We study the derangement graph $Γ_{n}$ whose vertex set consists of all permutations of ${1, \dots, n}$ , where two vertices are adjacent if and only if their corresponding permutati…

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

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

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

Degree Power Sums in Extremal Set Systems

Projective Ore-Degree Conditions for Intersection Theorems in Vector Spaces

Matchings and Near-Optimal 2-Factor Packings in Percolated Vertex-Transitive Graphs

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

Counting sunflowers with restricted matching number

Edge pancyclic Cayley graphs on symmetric group

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

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

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

Simplices in $t$ -intersecting families for vector spaces