Mei Lu

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10 papers · 1 filter

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

Convex Transference for Degree Powers 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…

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…

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

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

Convex Transference for Degree Powers 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

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

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