Mei Lu

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…

Counting induced subgraphs with given intersection sizes

Haixiang Zhang, Yichen Wang, Xiamiao Zhao +1

Let $F$ be a graph of order $r$ . In this paper, we study the maximum number of induced copies of $F$ with restricted intersections, which highlights the motivation from extremal se…

Generalized TurÃ¡n problems for a matching and long cycles

Xiamiao Zhao, Mei Lu

Let $F$ be a family of graphs. A graph $G$ is $F$ -free if $G$ does not contain any $F \in F$ as a subgraph. The general TurÃ¡n number, denoted by $ex(n…

Anti-Ramsey problems in the generalized Petersen graphs for cycles

Huiqing Liu, Mei Lu, Shunzhe Zhang

The anti-Ramsey number $A r (G, H)$ is the maximum number of colors in an edge-coloring of $G$ with no rainbow copy of $H$ . In this paper, we determine the exact anti-Ramsey number in…

math.CO2013

Algebraic Cayley Graphs over Finite Fields

Mei Lu, Daqing Wan, Li-Ping Wang +1

A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new…

#vector spaces#finite fields#intersecting families#erdos-ko-rado theorem

Projective Ore-Degree Conditions for Intersection Theorems in Vector Spaces

Mengyu Cao, Mei Lu, Xuyang Yan +1

The paper introduces a projective Ore-degree measure for families of k‑dimensional subspaces over a finite field and proves sharp analogues of the Erdős–Ko–Rado and Hilton–Milner i…

TurÃ¡n number of complete bipartite graphs with bounded matching number

Huan Luo, Xiamiao Zhao, Mei Lu

Let $F$ be a family of graphs. A graph $G$ is $F$ -free if $G$ does not contain any $F \in F$ as a subgraph. The TurÃ¡n number $e x (n, F)$ is t…

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…

$w$ -Dominating Set Problem on Graphs of Bounded Treewidth

Ke Liu, Mei Lu

Let $G = (V, E)$ be a graph. Let $w$ be a positive integer. A $w$ -dominating set is a vertex subset $S$ such that for all $v \in V$ , either $v \in S$ or it has at least $w$ neighbors in…

quant-ph2014

Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity

Mei Lu, Yan Xia, Li-Tuo Shen +2

We use the approach of "transitionless quantum driving" proposed by Berry to construct shortcuts to the population transfer and the creation of maximal entanglement between two $Î…

Counting sunflowers with restricted matching number

Haixiang Zhang, Mengyu Cao, Mei Lu

For a family $H \subseteq (k [ n ])$ , a subset ${A_{1}, A_{2}, \dots, A_{m}} \subseteq H$ is called a \textit{matching} of size~ $m$ if the sets $A_1, A_2, \ld…

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…

TurÃ¡n type problems for a fixed graph and a linear forest

Haixiang Zhang, Xiamiao Zhao, Mei Lu

Let $F$ be a family of graphs. A graph $G$ is $F$ -free if $G$ does not contain any $F \in F$ as a subgraph. The TurÃ¡n number, denoted by $ex(n, \maths…

Edge version of the inducibility via the entropy method

Yichen Wang, Xiamiao Zhao, Mei Lu

The inducibility of a graph $H$ is about the maximum number of induced copies of $H$ in a graph on $n$ vertices. We consider its edge version, that is, the maximum number of induce…

The Rainbow Saturation Number of Cycles

Yiduo Xu, Zhen He, Mei Lu

An edge-coloring of a graph $H$ is a function $C : E (H) \to N$ . We say that $H$ is rainbow if all edges of $H$ have different colors. Given a graph $F$ , a…

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…

The generalized Tur'{a}n number of long cycles in graphs and bipartite graphs

Changchang Dong, Mei Lu, Jixiang Meng +1

Given a graph $T$ and a family of graphs $F$ , the maximum number of copies of $T$ in an $F$ -free graph on $n$ vertices is called the generalized TurÃ¡n number,…

Vertex degree sums for rainbow matchings in 3-uniform hypergraphs

Haorui Liu, Mei Lu, Yan Wang +1

Let $n \in 3 Z$ be sufficiently large. Zhang, Zhao and Lu proved that if $H$ is a 3-uniform hypergraph with $n$ vertices and no isolated vertices, and if $deg(u)+deg(v) > \…

quant-ph2013

Driving three atoms into a singlet state in an optical cavity via adiabatic passage of a dark state

Mei Lu, Yan Xia, Jie Song +1

In this paper, we propose an efficient scheme to drive three atoms in an optical cavity into a singlet state via adiabatic passage. Appropriate Rabi frequencies of the classical fi…

Extremal results on Berge disjoint paths

Xiamiao Zhao, Yiyan Zhan, Mei Lu

The well-known ErdÅs-Gallai Theorem gave the TurÃ¡n number of paths. Bushaw and Kettle generalized this result to consider the TurÃ¡n number of disjoint paths. Since then, many st…

Shadows of Uniform Hypergraphs under a Minimum Degree Condition

Haorui Liu, Mei Lu, Yi Zhang

Given a set $X$ and an integer $t$ , let $F$ be a family of $k$ -subsets of $X$ . The Kruskal--Katona theorem implies that if $∣ F ∣ \geq (k t)$ , then $|\parti…

Partite saturation number of cycles

Yiduo Xu, Zhen He, Mei Lu

A graph $H$ is said to be $F$ -saturated relative to $G$ , if $H$ does not contain any copy of $F$ , but the addition of any edge $e$ in $E (G) \ E (H)$ would create a copy of $…

Linear recoloring diameter of degenerate chordal graphs and bounded treewidth graphs

Yichen Wang, Mei Lu

Let $G$ be a graph on $n$ vertices and $t$ an integer. The reconfiguration graph of $G$ , denoted by $R_{t} (G)$ , consists of all $t$ -colorings of $G$ and two $t$ -colorings are adjacen…

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.CO2016

Properties of Catlin's reduced graphs and supereulerian graphs

Wei-Guo Chen, Zhi-Hong Chen, Mei Lu

A graph $G$ is called collapsible if for every even subset $R \subseteq V (G)$ , there is a spanning connected subgraph $H$ of $G$ such that $R$ is the set of vertices of odd degree i…

quant-ph2020

Enhancement of spontaneous entanglement generation via coherent quantum feedback

Bin Zhang, Sujian You, Mei Lu

We investigate the entanglement dynamics of two two-level emitters (qubits) mediated by a semiinfinite, one-dimensional (1D) photonic waveguide. The coupling of each qubit to the w…

Edge pancyclic Cayley graphs on symmetric group

Mengyu Cao, Mei Lu, Zequn Lv +1

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

math.CO2023

ErdÅs-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…

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…

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…

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.CO2015

Some bounds on the eigenvalues of uniform hypergraphs

Xiying Yuan, Man Zhang, Mei Lu

Let $H$ be a uniform hypergraph. Let $A (H)$ and $Q (H)$ be the adjacency tensor and the signless Laplacian tensor of $H$ , respectively. In th…

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

Mengyu Cao, Mei Lu, Haixiang Zhang

Let $H$ be a fixed graph with $q = e (H) \geq 3$ and containing two adjacent edges, and let $ℓ \geq q$ be fixed. We establish an entropy-transference principle for rainbow- $H$ -free edge…

quant-ph2013

Generation of N-atom W-class states in spatially separated cavities

Mei Lu, Yan Xia, Jie Song +1

We propose a feasible and efficient scheme to generate $N$ -atom $W$ -class states in spatially separated cavities without using any classical driving pulses. We adopt the model in w…

math.CO2019

Edge-bipancyclicity of bubble-sort star graphs

Jia Guo, Mei Lu

The interconnection network considered in this paper is the bubble-sort star graph. The $n$ -dimensional bubble-sort star graph $B S_{n}$ is a bipartite and $(2 n - 3)$ -regular graph of o…

A polynomial time algorithm to find star chromatic index on bounded treewidth graphs with given maximum degree

Yichen Wang, Mei Lu

A star edge coloring of a graph $G$ is a proper edge coloring with no 2-colored path or cycle of length four. The star edge coloring problem is to find an edge coloring of a given…

The saturation number of wheels

Yanzhe Qiu, Zhen He, Mei Lu +1

A graph $G$ is said to be $F$ -free, if $G$ does not contain any copy of $F$ . $G$ is said to be $F$ -semi-saturated, if the addition of any nonedge $e \neq \in E (G)$ would create a n…

The Minimum Weighting Ratio Problem and Its Application in Chordal Graphs

Hui Lei, Mei Lu, Yongtang Shi +2

Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related res…

On graphs with exactly one anti-adjacency eigenvalue and beyond

Jianfeng Wang, Xingyu Lei, Mei Lu +2

The anti-adjacency matrix of a graph is constructed from the distance matrix of a graph by keeping each row and each column only the largest distances. This matrix can be interpret…

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.CO2019

On the anti-Ramsey number of forests

Chunqiu Fang, Ervin GyÅri, Mei Lu +1

We call a subgraph of an edge-colored graph rainbow subgraph, if all of its edges have different colors. The anti-Ramsey number of a graph $G$ in a complete graph $K_{n}$ , denoted…

quant-ph2014

Ground state of the asymmetric Rabi model in the ultrastrong coupling regime

Li-Tuo Shen, Zhen-Biao Yang, Mei Lu +2

We study the ground states of the single- and two-qubit asymmetric Rabi models, in which the qubit-oscillator coupling strengths for the counterrotating-wave and corotating-wave in…

A Quadratic Vertex Threshold for Isolated Cliques in the Minimum Degree Kruskal-Katona Problem for 3-Uniform Hypergraphs

Haorui Liu, Mei Lu, Yi Zhang

Given a set $X$ and an integer $t$ , let $F$ be a family of $k$ -subsets of $X$ . The Kruskal-Katona theorem states that if $∣ F ∣ \geq (k t)$ , then $|\partial…

A generalization of ErdÅs-Hajnal problem on paths with equal-degree endpoints

Xiamiao Zhao, Yichen Wang, Mei Lu

ErdÅs and Hajnal proposed a problem that: is it true that every $(2 n + 1)$ -vertex graph with $n^{2} + n + 1$ edges contains two vertices of equal degree connected by a path of length thre…

The maximum sum of sizes of non-empty cross $L$ -intersecting families

Xiamiao Zhao, Haixiang Zhang, Mei Lu

Let $n$ , $r$ , and $k$ be positive integers such that $k, r \geq 2$ , $L$ a non-empty subset of $[k]$ , and $F_{i} \subseteq (k [ n ])$ for $1 \leq i \leq r$ . We say that…

quant-ph2013

Using shortcut to adiabatic passage for the ultrafast quantum state transfer in cavity QED system

Mei Lu, Li-Tuo Shen, Yan Xia +1

We propose an alternative scheme to implement the quantum state transfer between two three-level atoms based on the invariant-based inverse engineering in cavity quantum electronic…

All minimum $C_{4}$ -saturated multipartite graphs

Yiduo Xu, Zhen He, Mei Lu +1

A subgraph $H$ of $G$ is said to be $F$ -saturated relative to $G$ , if $H$ does not contain any copy of $F$ , but the addition of any edge $e$ in $E (G) \ E (H)$ would create a…

On the total Italian domination number in digraphs

Changchang Dong, Yubao Guo, Mei Lu +1

Consider a finite simple digraph $D$ with vertex set $V (D)$ . An Italian dominating function (IDF) on $D$ is a function $f : V (D) \to {0, 1, 2}$ satisfying every vertex $u$ with…

Algorithm for finding vertex-edge domination number on graphs with bounded treewidth and related problems on planar graphs

Yichen Wang, Haixiang Zhang, Mei Lu

Given a graph $G = (V, E)$ , a vertex $u \in V$ {\em ve-dominates} all edges incident to any vertex of $N_{G} [u]$ . A set $S \subseteq V$ is a {\em ve-dominating set} if for all edges $e\…

$r$ -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.CO2015

Two coloring problems on matrix graphs

Zhe Han, Mei Lu

In this paper, we propose a new family of graphs, matrix graphs, whose vertex set $F_{q}^{N \times n}$ is the set of all $N \times n$ matrices over a finite field $\mathbb{F}_…

math.CO2017

Vertex degree sums for perfect matchings in 3-uniform hypergraphs

Yi Zhang, Yi Zhao, Mei Lu

We determine the minimum degree sum of two adjacent vertices that ensures a perfect matching in a 3-graph without isolated vertex. More precisely, suppose that $H$ is a 3-uniform h…

Degree-restricted semi-saturation numbers of cliques and its applications

Zhen He, Mei Lu, Yanzhe Qiu +1

A graph $G$ is said to be $F$ -semi-saturated if the addition of any nonedge $e \neq \in E (G)$ would create a new copy of $F$ in $G + e$ . The semi-saturation number $ss a t (n, F)$ is the…

Rainbow Independent Sets in Cycles

Zequn Lv, Mei Lu

For a given class $C$ of graphs and given integers $m \leq n$ , let $f_{C} (n, m)$ be the minimal number $k$ such that every $k$ independent $n$ -sets in any graph belonging…

math.CO2014

Linearized Wenger graphs

Xiwang Cao, Mei Lu, Daqing Wan +2

Motivated by recent extensive studies on Wenger graphs, we introduce a new infinite class of bipartite graphs of the similar type, called linearized Wenger graphs. The spectrum, di…

#intersecting families#degree powers#extremal set theory#codegree

Convex Transference for Degree Powers in Extremal Set Systems

Mengyu Cao, Mei Lu, Haixiang Zhang

The paper introduces a discrete two‑moment interpolation technique to bound sums of degree powers in intersecting families and shows that full star families uniquely maximize these…

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.CO2019

Vertex degree sums for matchings in 3-uniform hypergraphs

Yi Zhang, Yi Zhao, Mei Lu

Let $n, s$ be positive integers such that $n$ is sufficiently large and $s \leq n /3$ . Suppose $H$ is a 3-uniform hypergraph of order $n$ . If $H$ contains no isolated vertex and $deg(…

#hypergraph matching#degree conditions#k-uniform hypergraphs#extremal combinatorics

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

Haixiang Zhang, Mengyu Cao, Mei Lu

The paper establishes degree sequence and Ore-degree conditions that guarantee a k‑uniform hypergraph contains a matching of a given size, improving previous bounds and showing the…

The treewidth of 2-section of hypergraphs

Ke Liu, Mei Lu

Let $H = (V, F)$ be a simple hypergraph without loops. $H$ is called linear if $∣ f \cap g ∣ \leq 1$ for any $f, g \in F$ with $f \neq = g$ . The $2$ -section of $H$ , denoted by $[H]_{2}$ , is a gra…

Inversion diameter and treewidth

Yichen Wang, Haozhe Wang, Yuxuan Yang +1

In an oriented graph $G$ , the inversion of a subset $X$ of vertices is the operation that reverses the orientation of all arcs with both end-vertices in $X$ . The i…

#hypergraph matching#extremal combinatorics#t-matching number#erdos matching conjecture

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

Mengyu Cao, Mei Lu, Haixiang Zhang

The paper determines the maximum number of edges in a k‑uniform hypergraph with a prescribed t‑matching number, extending the Erdős Matching Conjecture, and also identifies the sec…