Mengyu Cao

activity

20192022

t

-intersecting families for vector spaces

5 citations · 13 across the 14 of their papers we have counts for

collaborators

14 papers

math.CO2022

Triangles in r-wise t-intersecting families

Jiaqi Liao, Mengyu Cao, Mei Lu

Let $t$ , $r$ , $k$ and $n$ be positive integers and $F$ a family of $k$ -subsets of an $n$ -set $V$ . The family $ \CF $ is $r$ -wise $t$ -intersecting if for any $ F_1, \l…

math.CO2022★ 1 cited

On the $P_{3}$ -hull numbers of $q$ -Kneser graphs and Grassmann graphs

Jiaqi Liao, Mengyu Cao, Mei Lu

Let $S$ be an $n$ -dimensional vector space over the finite field $F_{q}$ , where $q$ is necessarily a prime power. Denote $K_{q} (n, k)$ (resp. $J_{q} (n, k)$ ) to be the \emph{ $q$ -Kn…

math.CO2022

$r$ -cross $t$ -intersecting families for vector spaces

Mengyu Cao, Mei Lu, Benjian Lv +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 $V$ . The families $\mathcal…

math.CO2021

Non-trivial $t$ -intersecting families for the distance-regular graphs of bilinear forms

Mengyu Cao, Benjian Lv, Kaishun Wang

Let $V$ be an $(n + ℓ)$ -dimensional vector space over a finite field, and $W$ a fixed $ℓ$ -dimensional subspace of $V$ . Write $[n , 0 V]$ to be the set of all $n$ -dimensiona…

math.CO2021★ 1 cited

Two characterizations of the grid graphs

Brhane Gebremichel, Meng-Yue Cao, Jack H. Koolen

In this paper we give two characterizations of the $p \times q$ -grid graphs as co-edge-regular graphs with four distinct eigenvalues.

math.CO2021★ 1 cited

Maximality of Seidel matrices and switching roots of graphs

Meng-Yue Cao, Jack H. Koolen, Akihiro Munemasa +1

In this paper, we discuss maximality of Seidel matrices with a fixed largest eigenvalue. We present a classification of maximal Seidel matrices of largest eigenvalue $3$ , which giv…

math.CO2021

Treewidth of the $q$ -Kneser graphs

Mengyu Cao, Ke Liu, Mei Lu +1

Let $V$ be an $n$ -dimensional vector space over a finite field $F_{q}$ , where $q$ is a prime power. Define the \emph{generalized $q$ -Kneser graph} $K_{q} (n, k, t)$ to be the gra…

math.CO2020★ 1 cited

Recent progress on graphs with fixed smallest eigenvalue

Jack H. Koolen, Meng-Yue Cao, Qianqian Yang

We give a survey on graphs with fixed smallest eigenvalue, especially on graphs with large minimal valency and also on graphs with good structures. Our survey mainly consists of th…

math.CO2020★ 1 cited

Treewidth of the generalized Kneser graphs

Ke Liu, Mengyu Cao, Mei Lu

Let $n$ , $k$ and $t$ be integers with $1 \leq t < k \leq n$ . The \emph{generalized Kneser graph} $K (n, k, t)$ is a graph whose vertices are the $k$ -subsets of a fixed $n$ -set, where tw…

math.CO2020

Extremal even-cycle-free subgraphs of the complete transposition graphs

Mengyu Cao, Benjian Lv, Kaishun Wang +1

Given graphs $G$ and $H$ , the generalized Turán number $ex (G, H)$ is the maximum number of edges in an $H$ -free subgraph of $G$ . In this paper, we obtain an asymptotic upper b…

math.CO2020★ 2 cited

The structure of large non-trivial t-intersecting families for finite sets

Mengyu Cao, Benjian Lv, Kaishun Wang

In this paper, we describe the structure of maximal non-trivial uniform $t$ -intersecting families with large size for finite sets. In the special case when $t = 1$ , our result gives…

math.CO2020★ 5 cited

Non-trivial $t$ -intersecting families for vector spaces

Mengyu Cao, Benjian Lv, Kaishun Wang +1

Let $V$ be an $n$ -dimensional vector space over a finite field $F_{q}$ . In this paper we describe the structure of maximal non-trivial $t$ -intersecting families of $k$ -dimen…

math.CO2019★ 1 cited

On even-cycle-free subgraphs of the doubled Johnson graphs

Mengyu Cao, Benjian lv, Kaishun Wang

The generalized Turán number $ex (G, H)$ is the maximum number of edges in an $H$ -free subgraph of a graph $G .$ It is an important extension of the classical Turán number ${\rm…

math.CO2019

Some Remarks on Systems of Equiangular Lines

Mengyue Cao, Jack H. Koolen, Jae Young Yang

In this note, we study the maximum number $N_{α} (d)$ of a system of equiangular lines in $R^{d}$ with cosine $α$ , where $\frac{1}{α}$ is not an odd positive integer. This note i…