江苏师大70周年校庆系列学术讲座(一百一十)

文章作者:  发布时间: 2022-11-23  浏览次数: 10

报 告 人:宋梓霞 教授 

报告题目:Coloring Graphs with Forbidden Minors

报告时间:2022年11月25日(周五)上午09:30

报告地点:腾讯会议:203-886-314 会议密码:221125 

主办单位:数学与统计学院、科学技术研究院

报告人简介:

     宋梓霞,美国 University of Central Florida数学系教授,博士生导师,主要研究领域为图论。2000-2004年在美国Georgia Institute of Technology获算法组合优化博士学位,2004-2005年在美国The Ohio State University数学系从事博士后研究。2005年授聘于美国University of Central Florida数学系,获得2009-2011美国NSA科研基金和2019-2022美国NSF科研基金,是美国自然科学基金(NSF)的基金评委,获校优秀教师奖和科研奖。在Journal of Combinatorial Theory、Series B、Combinatorica、SIAM Journal on Discrete Mathematics、Journal of Graph Theory等图论组合领域顶尖杂志发表SCI论文多篇。

报告摘要: 

     Hadwiger’s Conjecture from 1943 states that every graph with no Kt minor is (t−1)-colorable; it remains wide open for all t ≥ 7. For positive integers t and s, let Kt −s denote the family of graphs obtained from Kt by removing s edges. We say that a graph G has no Kt −s minor if it has no H minor for every H ∈ Kt −s . Jakobsen in 1971 proved that every graph with no K7 −2 minor is 6-colorable. In this talk, we consider the next two steps and present our recent work that every graph with no K8 −4 minor is 7-colorable, and every graph with no K9 −6 minor is 8-colorable. Our result implies that H-Hadwiger’s Conjecture, suggested by Paul Seymour in 2017, is true for all graphs H on eight vertices such that H is a subgraph of every member in K8 −4 , and all graphs H on nine vertices such that H is a subgraph of every member in K9 −6 . This is joint work with Michael Lafffferty.