学术报告
报告题目：Graphs whose size is the Turan number plus one
报告人：詹兴致教授华东师范大学
报告时间：2020/11/27(周五)下午 14:00-15:00
报告形式：腾讯会议
会议ID：818 501 543
报告摘要：We consider finite simple graphs. Given a graph H and a positive integer n, the Turan number of H for the order n, denoted ex(n,H), is the maximum size of a graph of order n not containing H as a subgraph. Erd\H{o}s posed the following problem in 1990: ``For which graphs H is it true that every graph on n vertices andex(n,H)+1 edges contains at least two Hs? Perhaps this is always true. We solve the second part of this problem in the negative by proving that for every integer k at least 4, there exists a graph H of order k and at least two orders n such that there exists a graph of order n and sizeex(n,H)+1 which contains exactly one copy of H. We also consider the problem with H being the 4-cycle. This is joint work with Pu Qiao.
报告人简介：詹兴致，华东师范大学教授，是国际上矩阵分析领域领头专家之一。曾在Springer出版专著《Matrix Inequalities》和在美国数学会出版《Matrix Theory》。代表性工作是解决了算子单调函数的Hiai猜想，发表在德国的Math. Ann.上。近年来转向图论，已经做出了一些有趣的结果。