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

collaborators

20 papers

math.GR2026

Automorphism groups of Cayley graphs on almost simple groups with normal connection sets

Mengyu Cao, Benjian Lv, Binzhou Xia

We determine the full automorphism group of every connected Cayley graph on an almost simple group with a normal connection set. We also characterize exactly when the full automorp…

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…

Automorphism groups of Cayley graphs on almost simple groups with normal connection sets

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