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天津大学宁博博士学术报告

信息来源: 暂无 发布日期: 2017-09-12 浏览次数:

报告人:宁博,讲师,天津大学

报告时间:2017年9月15日14:30-16:30  

报告地点:数计学院4号楼229室

报告题目:Stability versions of Erdos’ theorem and Woodall’s conjecture on  cycles

报告人简介:宁博,西北工业大学理学博士,2011届福州大学离散数学中心硕士。2015年7月入职天津大学,任讲师。主要研究领域是结构图论、极值图论和图谱理论,特别是圈结构的存在性。在SCI源刊物发表(含接受)论文30余篇。现主持国家自然科学基金青年基金一项,参与面上项目一项。

报告摘要:Erdos  (1962) proved a Turan-type theorem on Hamilton cycle in terms of minimum degree  and the number of edges of a graph. Generalizing Erdos' result, Woodall (1976)  conjectured that: For a 2-connected graph G on n vertices with $\delta(G)\geq  k$, there holds $e(G)\leq \max\{f(n,k,c),f(n,\lfloor\frac{c}{2}\rfloor,c)\}$ if  $c(G)=c\leq n-1$, where $f(n,k,c):=\binom{c-k+1}{2}+k\cdot (n-c+k-1)$. In this  talk, we present stability versions of Erdos' theorem and Woodall's conjecture,  respectively. Our result implies a proof of Woodall's conjecture and also  generalizes recent theorems of Furedi, Kostochka, Verstraete (2016) and Furedi,  Kostochka, Luo, Verstraete (2017+).We also give a stability version of a  classical theorem of Bondy (1971/1972) on long cycles. Our methods are  completely different from Furedi et al.