腾讯会议：526-334-972
题目：D-magic labelings of Distance-Regular Graphs
摘要： Let $G$ be a finite undirected simple connected graph with vertex set $V(G)$, distance function $\partial$ and diameter $d$. Let $D\subseteq\{0,1,\dots,d\}$ be a set of distances. A bijection $l:V(G)\rightarrow\{1,2,\dots,|V(G)|\}$ is called a $D$-magic labeling of $G$ if there exists a constant $k$ such that $\sum\limits_{x\in N_D(v)}l(x)=k$ for any vertex $v\in V(G)$, where $N_D(v)=\{x\in V(G): \partial(x,v)\in D\}$. We say $G$ has a $D$-magic labeling if $G$ admits a $D$-magic labeling. In this talk,
we give the necessary and suffieient conditions for the folded $n$-cube and the halved folded n-cube to have a $\{1\}$-magic labeling and a $\{0,1\}$-magic labeling, respectively.
This is a joint work with Yi Tian, Na kang, Bo Hou, Lihang Hou, Weili Wu and Dingzhu Du.
个人简介：高锁刚，河北师大女王调教
教授、博士生导师。研究领域：代数组合、组合优化，美国UTD大学、日本ICU大学访问学者。在组合数学著名期刊J. Combin. Theory A、 European J. Combin.、J. Global Optim. 等期刊发表论文100余篇。在科学出版社出版专著一部，担任国际期刊DMAA杂志编委。主持完成三项国家自然科学基金、一项教育部博士点基金、两项河北省自然科学基金。作为第一完成人获河北省科学技术奖二等奖1项、三等奖1项。
题目：Approximation Algorithms for Minimum Weight Connected Dominating Set
摘要：A connected dominating set (CDS) of a graph G is a vertex set C such that every vertex in $V(G)\backslash C$ has at least one neighbor in C and the subgraph of G induced by C is connected. The goal of the minimum weight connected dominating set problem (MinWCDS) is to find a CDS with the minimum total vertex weight. The best previously known approximation ratio for MinWCDS is $(1.35+\varepsilon)ln(n)$, due to Guha and Khuller in 1999. In this talk, I’ll introduce our recent result which breaks the barrier of $ln(n)$, improving the ratio to $2ln\triangle$, where $\triangle$ is the maximum degree of the graph (note that in general, $\triangle$ is much smaller than $n$).
个人简介：张昭，浙江师范大学杰出教授，浙江省“钱江学者”特聘教授。主要研究方向为离散优化算法设计与分析，发表学术论文200余篇，被SCI索引140余篇。主持完成了4项国家自然科学基金项目和4项教育部项目，目前主持1项国家自然科学联合基金重点项目。曾获国家自然科学优秀青年基金，入选教育部新世纪优秀人才支持计划，新疆科技进步一等奖等。第八届国务院学位办数学学科评议组成员、中国运筹学会常务理事、中国运筹学会数学规划分会副理事长等。
