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数学学科离散数学研究所学术报告(ALI TAHERKHAN,Shahid Behshti University)

发布者:付慧娟   发布时间:2019-12-23  浏览次数:87


报告题目:SIZE AND STRUCTURE OF LAGE G-FREE INDUCED SUBGRAPHS OF

KNESER GRAPHS

报告 人: ALI TAHERKHANI 

报告时间:2019年12月24日(星期二)下午14:30-15:30

报告地点:21幢427


报告内容:The Kneser graph KGn;k  is a graph whose vertex set is the family of all k -subsets of [n ] and two vertices are adjacent if their corresponding subsets are disjoint. The celebrated Erd}os-Ko-Rado theorem determines the size and structure of a maximum induced K2 -free subgraph (the maximum independent set) in KGn;k . As a generalization of the Erd}os-Ko-Rado theorem, Erd}os proposed a conjecture about the maximum cardinality of an induced Ks+1 -free subgraph of KGn;k , the Erd}os matching conjecture. In this talk we consider the problem of determining the structure of a maximum family A  for which KGn;k [A ] contains no subgraph isomorphic to a given graph G . In this regard, we determine the size and structure of such a family provided that n  is su_ciently large with respect to G  and k . As an extension of the Erd}os-Ko-Rado theorem, the Hilton-Milner theorem determines the size and structure of the second largest maximal independent set in Kneser graphs. We will present some our recent results about the size and structure of some large Ks;t -free induced subgraphs in Kneser graphs. Our results are nontrivial extensions of some recent generalizations of the Erd}os-Ko-Rado theorem and the Hilton-Milner theorem such asthe Han and Kohayakawa theorem [Proc. Amer. Math. Soc. 145 (2017), pp. 73{87] which _nds the structure of the third largest independent set of Kneser graphs, the Kostochka and Mubayi theorem [Proc. Amer. Math. Soc. 145 (2017), pp. 2311{2321], and the more recent Kupavskii's theorem [arXiv:1810.009202018 (2018)] whose both results determine the size and structure of the i th largest independent set of Kneser graphs for i _ k  + 

个人概况:ALI TAHERKHANI,男,博士,毕业于Shahid Behshti University,研究领域为图着色,组合学中的概率方法,代数组合,拓扑组合及其相互联系。


邀请人:朱绪鼎



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