报告题目：Minimum Degree Stability of Graphs Forbidding Some Odd Cycles

报 告 人：彭岳建 ，湖南大学

报告摘要：We determine what the tight bound on the minimum degree would be to guarantee an n-vertex graph forbidding a family of odd cycles to be bipartite. Let C be a family of odd cycles. We discover that the length of the shortest odd cycle not in C and the length of the longest odd cycle in C determine what the tight bound is. Our result is also related to the question of Erd˝os and Simonovits: For an integer r ≥ 2 and a family of non-bipartite graphs H, what is the tight bound of α such that any H-free n-vertex graph with minimum degree at least αn has chromatic number at most r? Our result answers this question for r = 2 and any family of odd cycles. This is a joint work with Xiaoli Yuan.

报告人简介：彭岳建，湖南大学教授、博士生导师。2001年于美国埃默里大学（Emory University）获得理学博士学位。2002-2012年在美国印第安纳州立大学（Indiana State University）历任助理教授、副教授、教授（终身）。2012年作为“湖南省百人计划”特聘教授回到湖南大学。彭岳建教授的主要研究方向是极值组合与图论，在国际组合图论权威刊物JCTB、JCTA、JGT等发表论文40多篇。目前主持国家自然科学基金重点项目一项。

报告时间：2023年6月17日 9:00-10:00

报告地点：文渊楼A231

主办单位：伟德国际1946源自英国