arXiv subjects

Meiqin Wang

Publications and source records attributed to Meiqin Wang.

3 recordsLinked to original sources

arXiv2026

The maximum number of maximal dissociation sets in trees

Let $G$ be a simple graph. A dissociation set of $G$ proposed by Yannakakis in $1981$ is defined as a set of vertices that induces a subgraph in which every vertex has a degree of at most $1$. A dissociation set is maximal if it is not contained as a proper subset in any other dissociation set. In $2025$, Wang et al.\cite{ZiyuanWang} established that for any tree $T$ of order $n\geq 4$, the number of maximal dissociation sets in $T$ is at most $3^{\frac{n-1}{3}}+\frac{n-1}{3}$ and characterized the extremal trees attaining the upper bound. They also proposed a conjecture about the upper bound of the maximal dissociation set. In this paper, we consider this conjecture and show that the maximum number of maximal dissociation sets in a tree of order $n(n\geq 3)$ is $g(n)$, where \[ g(n) = \begin{cases} n, & n=3,4,5,6,\\ 3^{\frac{n-1}{3}}+\frac{n-1}{3}, & n \equiv 1 \pmod{3},~n\geq7,\\ 4\cdot 3^{\frac{n-5}{3}}+n-5, & n \equiv 2 \pmod{3},~n\geq8, \\ 16\cdot 3^{\frac{n-9}{3}}+3n-25, & n \equiv 0 \pmod{3},~n\geq12~\text{and }~n\neq21, \\ 19, & n=9, \\ 1349, & n=21. \end{cases} \] We also characterize the extremal trees with the maximum number of maximal dissociation sets.

math.CO↗

arXiv2024

Exact values and improved bounds on $k$-neighborly families of boxes

A finite family $\mathcal{F}$ of $d$-dimensional convex polytopes is called $k$-neighborly if $d-k\le\textup{dim}(C\cap C')\le d-1$ for any two distinct members $C,C'\in\mathcal{F}$. In 1997, Alon initiated the study of the general function $n(k,d)$, which is defined to be the maximum size of $k$-neighborly families of standard boxes in $\mathbb{R}^{d}$. Based on a weighted count of vectors in $\{0,1\}^{d}$, we improve a recent upper bound on $n(k,d)$ by Alon, Grytczuk, Kisielewicz, and Przesławski for any positive integers $d$ and $k$ with $d\ge k+2$. In particular, when $d$ is sufficiently large and $k\ge 0.123d$, our upper bound on $n(k,d)$ improves the bound $\sum_{i=1}^{k}2^{i-1}\binom{d}{i}+1$ shown by Huang and Sudakov exponentially. Furthermore, we determine that $n(2,4)=9$, $n(3,5)=18$, $n(3,6)=27$, $n(4,6)=37$, $n(5,7)=74$, and $n(6,8)=150$. The stability result of Kleitman's isodiametric inequality plays an important role in the proofs.

math.CO↗

arXiv2020

SCNet: A Neural Network for Automated Side-Channel Attack

The side-channel attack is an attack method based on the information gained about implementations of computer systems, rather than weaknesses in algorithms. Information about system characteristics such as power consumption, electromagnetic leaks and sound can be exploited by the side-channel attack to compromise the system. Much research effort has been directed towards this field. However, such an attack still requires strong skills, thus can only be performed effectively by experts. Here, we propose SCNet, which automatically performs side-channel attacks. And we also design this network combining with side-channel domain knowledge and different deep learning model to improve the performance and better to explain the result. The results show that our model achieves good performance with fewer parameters. The proposed model is a useful tool for automatically testing the robustness of computer systems.

cs.CR↗