报 告 人：赵海兴，青海师范大学教授，博士生导师
报告题目：Research on Reliability of2-terminal Networks
报告时间：2021年12月30日（周四）上午8：30-11：30
报告地点：腾讯会议 ID：954468419
主办单位：数学与统计学院、科学技术研究院
报告人简介：
赵海兴，现任青海师范大学副校长、教授、博士生导师。享受国务院政府特殊津贴专家，教育部新世纪优秀人才，教育部“创新团队”负责人，青海省优先专家。担任全国运筹学会和组合与图论学会理事。主要从事网络科学和信息处理的研究工作，已主持完成1项科技部973前期研究专项、4项国家自然科学基金项目，其中2项成果获青海省科技进步二等奖和三等奖。已发表学术论文40余篇。
报告摘要：
A two-terminal graphG=(V,E) is a simple and undirected graph with two specified target vertices sand t in V. In G, if each edge survives independently with a fixed probabilityp, the two-terminal reliability is the probability that two target vertices areconnected. Let \mathcal{G}_{n,m} be the set of two-terminal graphs with nvertices and $m$ edges. An st-pathset of G is a subset of E that contains apath from s to t. Let N_i be the number of st-path sets of size i in G. Thetwo-terminal reliability polynomial of G\in \mathcal{G}_{n,m} can be written asR_2(G;p)=\sum_{i=0}^mN_ip^i(1-p)^{m-i}. A two-terminal graph G\in\mathcal{G}_{n,m} is uniformly most reliable if R_2(G;p)\geq R_2(H;p) for all H\in\mathcal{G}(n,m) and all p\in[0,1].
Betrandet al. [Networks 72 (2018) 200--216] proved that there is no uniformly mostreliable two-terminal graph if either n\geq11 and 20\leq m\leq 3n-9 or n\geq8and {n\choose2}-\lfloor(n-2)/2\rfloor\leq m\leq {n\choose2}-2. In this paper,we further prove that there is no uniformly most reliable two-terminal graph ifn\geq6 and 3n-6<m\leq\binom{n}{2}-2 in a different way.
邀 请 人：苗正科