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.
