时间2018年1月6号
地 点：数学科学学院38楼108
8:30--9:00 康丽英 上海大学
题目：Tensor and the spectral radius of uniform hypergraphs
9:00--9:30 王文环 上海大学
题目：The signless Laplacian coefficients and the incidence energy of the graphs without even cycles
9:45--10:15 单而芳 上海大学
题目：团超图的染色问题
10:15--10:45 柏春松 阜阳师范学院
题目：The semi-obnoxious 2-median problem on cactus graphs
11:00--11:30 梁作松 曲阜师范大学
题目：Advances in clique-coloring of graphs
11:30--12:00 董艳侠 上海对外经贸大学
题目：Extremal hypergraphs for matching number and domination number
14:30--15:00 吴领叶 《运筹学学报》编辑部
题目：《运筹学学报》基本情况介绍
15:00--15:30 程郁琨 苏州科技大学
题目：Agent Incentives of Strategic Behaviors in Resource Sharing
1.康丽英 上海大学
报告题目：Tensor and the spectral radius of uniform hypergraphs
摘要:
Let $\mathcal{A}(H)$ and $\mathcal{Q}(H)$ be the adjacency tensor and signless Laplacian tensor of an $r$-uniform hypergraph $H$. Denote by $\rho(H)$ and $\rho(\mathcal{Q}(H))$ the spectral radii of $\mathcal{A}(H)$ and $\mathcal{Q}(H)$, respectively. In this talk we present a lower bound on $\rho(H)$ in terms of vertex degrees and we characterize the extremal hypergraphs attaining the bound, which solves a problem posed by Nikiforov [V. Nikiforov, Analytic methods for uniform hypergraphs, Linear Algebra Appl. 457 (2014) 455-535]. Also, we prove a lower bound on $\rho(\mathcal{Q}(H))$ concerning degrees and give a characterization of the extremal hypergraphs attaining the bound. If $H$ is
connected, the unique positive eigenvector $x=(x_1,x_2,\cdots,x_n)^{\mathrm{T}}$ with
$||x||_r=1$ corresponding to spectral radius $\rho(H)$ is called the principal eigenvector
of $H$. The maximum and minimum entries of $x$ are denoted by $x_{\max}$ and $x_{\min}$,
respectively. We investigate the bounds of $x_{\max}$ and $x_{\min}$ in
the principal eigenvector of $H$. Meanwhile, we also obtain some bounds of the ratio
$x_i/x_j$ for $i$, $j\in [n]$ as well as the principal ratio $\gamma(H)=x_{\max}/x_{\min}$
of $H$.
Keywords: Uniform hypergraph; Adjacency tensor; Signless Laplacian tensor; Spectral radius
2.王文环 上海大学
报告题目：The signless Laplacian coefficients and the incidence energy of the graphs without even cycles
摘要:
Let $\Phi_{n,m}$ be set of the $(n,m)$-graphs without even cycles, where $n\leq m \leq \frac{3}{2}(n-1)$. We consider the signless Laplacian coefficients and the incidence energy in $\Phi_{n,m}$. A new graph transformation is proposed here. Among $\Phi_{n,m}$, it is obtained that there is exactly one minimal element with respect to the quasi-ordering according to their signless Laplacian coefficients. Furthermore, the graph with the minimal incidence energy is found among $\Phi_{n,m}$.
3.单而芳 上海大学
报告题目： 团超图的染色问题
摘要:
图的团染色也称为团超图染色。该报告介绍团超图的染色问题的主要研究进展情况和尚未解决的一些挑战性问题。
4.柏春松 阜阳师范学院
报告题目：Advances in clique-coloring of graphs
摘要:
Consider the semi-obnoxious $p$-meidan problem on cactus graphs. For the 2-median problem on a cactus graph with $n$ vertices, propose an algorithm of the time complexity $O(n^2)$.
5.梁作松 曲阜师范大学
报告题目：Advances in clique-coloring of graphs
摘要:
A maximal clique of $G$ is a clique not properly contained in any other clique. A $k$-clique-coloring of a graph $G$ is an assignment of $k$ colors to the vertices of $G$ such that no maximal clique with at least two vertices is monochromatic. The smallest integer $k$ admitting a $k$-clique-coloring of $G$ is called clique-coloring number of $G$. In this talk, we mainly introduce the recent advances in clique-coloring problem of planar graphs, perfect graphs and claw-free graphs.
6.董艳侠 上海对外经贸大学
报告题目：Extremal hypergraphs for matching number and domination number
摘要:
A matching in a hypergraph $\mathcal{H}$ is a set of pairwise disjoint hyperedges. The matching number $\nu(\mathcal{H})$ of $\mathcal{H}$ is the size of a maximum matching in $\mathcal{H}$. A subset $D$ of vertices of $\mathcal{H}$ is a dominating set of
$\mathcal{H}$ if for every $v\in V\setminus D$ there exists $u\in D$ such that $u$ and $v$ lie in an hyperedge of $\mathcal{H}$. The cardinality of a minimum dominating set of $\mathcal{H}$ is the domination number of $\mathcal{H}$, denoted by $\gamma(\mathcal{H})$. It was proved that $\gamma(\mathcal{H})\leq (r-1)\nu(\mathcal{H})$ for $r$-uniform hypergraphs and the 2-uniform hypergraphs (graphs) achieving equality $\gamma(\mathcal{H})=\nu(\mathcal{H})$ have been characterized. In
this paper we generalize the inequality $\gamma(\mathcal{H})\leq (r-1)\nu(\mathcal{H})$ to arbitrary hypergraph of rank $r$ and we completely characterize the extremal hypergraphs $\mathcal{H}$ of rank $3$ achieving equality $\gamma(\mathcal{H})=(r-1)\nu(\mathcal{H})$.
Keywords: Hypergraph; Matching; Domination; Transversal; Extremal hypergraph
7.吴领叶 《运筹学学报》编辑部
\centerline{报告题目： 《运筹学学报》基本情况介绍}
\centerline{摘要}
对《运筹学学报》来稿、审稿流程、出版流程、发行、宣传等情况做简单介绍。
8.程郁琨 苏州科技大学
报告题目： Agent Incentives of Strategic Behaviors in Resource Sharing
摘要:
In a resource sharing system, resources are shared among multiple interconnected peers. Peers act as both suppliers and customers of resources by making a certain amount of their resources directly available to other network participants. Their utilities are determined by the total amount of resources received from all neighbors. According to a preset mechanism, the allocation of the shared resources depends on the information that agents submit to the mechanism. The participating agents, however, may try to strategically manipulate its submitted information to influence the allocation with the expectation of its utility improvement. In this talk, we consider the tit-for-tat popular proportional response mechanism and discuss the incentives of agent strategic behaviors with the help of the concepts of truthfulness and incentive ratio.
