报告人：  宁博博士，天津大学

报告时间：2017年9月15日14:30

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

$e(G)\\leq \\max\\{f(n,k,c),f(n,\\lfloor\\frac{2}\floor,c)\\}$ 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.

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