【数学与统计及交叉学科前沿论坛------高端学术讲座第129场】

报告题目：Some Results on Second Neighborhood Conjucture in Digraph

报告人：蔡建生教授 潍坊学院4556银河国际在线

报告时间：2024年11月12日（周二）15:00-16:00

报告地点：腾讯会议 675-267-339

报告摘要：One of the most interesting open problems of digraph is Seymour's Second Neighbourhood Conjecture (SSNC), which asserts that every digraph $D$ has a vertex $v$ whose second out-neighbourhood $N^{++}(v)$ is greater than its out-neighbourhood $N^+(v)$ and we called such vertex $v$ a Seymour vertex. Sullivan stated two compromise conjectures on SSNC, a vertex $v$ satisfying conjecture of Sullivan is called a Sullivan-$i$ vertex for $i = 1, 2$. In this talk, we give a survey on SSNC, and we proved SSNC is true in some situation. And we also proved that every random tournament $T_n$ has $n$ Sullivan-$1$ vertices and at least $\frac{n}{2}-\sqrt{n\log{n}}$ Sullivan-2 vertices with high probability.

报告人简介：蔡建生，潍坊学院4556银河国际在线教授，中国工业与应用数学学会图论组合及其应用专业委员会常务委员、中国工业与应用数学学会信息和通讯领域的数学专业委员会委员、山东省数学会高等数学专业委员会常务理事、潍坊市五一劳动奖章获得者。长期从事图论和组合数学的研究，发表本专业学术论文80余篇，主持和参与国家自然科学基金项目多项，主持山东省自然科学基金项目多项。获得山东省自然科学三等奖一项，获得山东省高等学校优秀科研成果奖多项。