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学术报告: Exact bipartite Turan number of large even cycles

发布时间:2019年01月22日 浏览次数:发布者:mathky

报告人:宁博讲师 

          天津大学

题目: Exact bipartite Turan number of large even cycles

时间:2019年01月24日下午16:30

地点:海韵数理楼661

摘要: Let the bipartite Tur\'an number $ex(m,n,H)$ of a graph $H$ to be the maximum number of edges in an $H$-free bipartite graph with two parts of sizes $m$ and $n$. In this paper, we prove that $ex(m,n,C_{2t})=(t-1)n+m-t+1$ for any positive integers $m,n,t$, if $n\geq m\geq t\geq \frac{m}{2}+1$. This confirms the remaining part of a conjecture of Gy\"{o}ri (in a stronger form), and improves the upper bound of $ex(m,n,C_{2t})$ obtained by Jiang and Ma for this range. We also prove a tight edge condition for consecutive even cycles in bipartite graphs, which settles a conjecture by Adamus. As a main tool, for a longest cycle $C$ in a bipartite graph, we obtain an estimate on the upper bound of the number of edges which are incident to at most one vertex in $C$. Our two results generalize or sharp a classical theorem due to Jackson in different ways.

报告人简介:宁博,男,河南洛阳人。2015年入职天津大学,现任应用数学中心讲师。2011年福州大学离散数学中心硕士;2015年西北工业大学博士;2017-2018年南洋理工大学访问学者(半年)。主要在结构图论、极值图论和图谱理论等领域,特别是在子图存在性方向开展研究。在图论主流期刊SIAM J. Discrete Math., European J. Combin., Electronic J. Combin. 等发表论文30余篇。现主持国家级项目1项,其他项目2项。

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