Mengyue Cao

activity

20202026

most citedThe Lemmens-Seidel conjecture and forbidden subgraphs

2 citations · 3 across the 20 of their papers we have counts for

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19 papers · 1 filter

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

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

On Erdős--Ko--Rado and Hilton--Milner Theorems for Direct Products

Tian Yao, Mengyu Cao, Kaishun Wang

We investigate $t$ -intersecting families in direct-product set systems obtained by prescribing the number of selected elements in each part of a partitioned ground set. For a finit…

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

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…

math.CO2024

Treewidth of generalized Hamming graph, bipartite Kneser graph and generalized Petersen graph

Yichen Wang, Mengyu Cao, Zequn Lv +1

Let $t, q$ and $n$ be positive integers. Write $[q] = {1, 2, \dots, q}$ . The generalized Hamming graph $H (t, q, n)$ is the graph whose vertex set is the cartesian product of $n$ copie…

math.CO2023

Hilton-Milner theorem for $k$ -multisets

Jiaqi Liao, Zequn Lv, Mengyu Cao +1

Let $k, n \in N^{+}$ and $m \in N^{+} \cup {\infty}$ . A $k$ -multiset in $[n]_{m}$ is a $k$ -set whose elements are integers from ${1, 2, \dots, n}$ , an…

math.CO2023

Erdős-Ko-Rado Theorem for Bounded Multisets

Jiaqi Liao, Zequn Lv, Mengyu Cao +1

Let $k, m, n$ be positive integers with $k \geq 2$ . A $k$ -multiset of $[n]_{m}$ is a collection of $k$ integers from the set ${1, 2, \dots, n}$ in which the integers c…

math.CO2022★ 1 cited

Edge pancyclic derangement graphs

Zequn Lv, Mengyu Cao, Mei Lu

We consider the derangement graph in which the vertices are permutations of ${1, \dots, n}$ . Two vertices are joined by an edge if the corresponding permutations differ in every…

math.CO2022

Some intersection theorems for finite sets

Mengyu Cao, Mei Lu, Benjian Lv +1

Let $n$ , $r$ , $k_{1}, \dots, k_{r}$ and $t$ be positive integers with $r \geq 2$ , and $F_{i} (1 \leq i \leq r)$ a family of $k_{i}$ -subsets of an $n$ -set $V$ . The families $\mathcal…

math.CO2020★ 2 cited

The Lemmens-Seidel conjecture and forbidden subgraphs

Meng-Yue Cao, Jack H, Koolen +2

In this paper we show that the conjecture of Lemmens and Seidel of 1973 for systems of equiangular lines with common angle $arccos (1/5)$ is true. Our main tool is forbidden subgr…

A Near-Optimal Linear Range for the Erdős Matching Conjecture

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

On Erdős--Ko--Rado and Hilton--Milner Theorems for Direct Products

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

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

Treewidth of generalized Hamming graph, bipartite Kneser graph and generalized Petersen graph

Hilton-Milner theorem for k-multisets

Erdős-Ko-Rado Theorem for Bounded Multisets

Edge pancyclic derangement graphs

Some intersection theorems for finite sets

The Lemmens-Seidel conjecture and forbidden subgraphs

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

Hilton-Milner theorem for $k$ -multisets