报告题目1：On Seymour's and Sullivan's Second Neighbourhood Conjectures

报告人：王书晶，华中师范大学

报告时间：2025年10月14日（周二）15:00-16:00

报告地点：腾讯会议868 981 278

报告摘要：For a vertex $x$ of a digraph, $d^+(x)$ ($d^-(x)$, resp.) is the number of vertices at distance 1 from (to, resp.) $x$ and $d^{++}(x)$ is the number of vertices at distance 2 from $x$. In 1995, Seymour conjectured that for any oriented graph $D$ there exists a vertex $x$ such that $d^+(x)\leq d^{++}(x)$. In 2006, Sullivan conjectured that there exists a vertex $x$ in $D$ such that $d^-(x)\leq d^{++}(x)$. In this talk, we will give some results on this two conjectures.

报告人简介：王书晶，华中师范大学数统学院副教授，硕导，主要研究领域为极值图论、图谱理论。2022年10月到2023年9月到伦敦大学皇家霍洛威学院访问Gutin教授，合作领域为有向图的结构性质。主持国家自然科学基金青年项目1项，湖北省自然科学基金青年项目1项。在Journal of Graph Theory、Discrete Mathematics、Linear Algebra and its Applications等国际重要期刊发表文章20余篇学术论文。

报告题目2：Planar Turan Numbers of Configurations Involving $C_3$ and $\Theta_4$

报告人：高志鹏，西安电子科技大学

报告时间：2025年10月14日（周二）16:00-17:00

报告地点：腾讯会议868 981 278

报告摘要：The planar Tur\'{a}n number $\text{ex}_{\mathcal{P}}(n,H)$ is the maximum number of edges in an $n$-vertex $H$-free planar graph. While this value remains unknown for many large graphs (e.g., long paths or cycles), tight bounds are known for various small planar graphs, including cycles, paths, $\Theta$-graphs, and their unions. A representative case is $K_1 + L$, where $L$ is a linear forest without isolated vertices. Previous work has resolved the cases where $L$ is a path, a matching, or satisfies $|L| \geq 7$.

In this talk, we study $\text{ex}_{\mathcal{P}}(n,H)$ for graphs formed by combining $C_3$ and $\Theta_4$. We first consider $K_1 + (P_2 \sqcup P_3)$, which corresponds to one such configuration. Among the six possible configurations obtained from $C_3$ and $\Theta_4$, three have been solved previously. For the remaining three---including $K_1 + (P_2 \sqcup P_3)$---we establish tight bounds. Furthermore, we completely characterize the extremal graphs for two of these three cases.

报告人简介：高志鹏，博士，西安电子科技大学数学与统计学院教师，研究方向图论与组合优化，主要研究控制集及其相关问题。在Journal of Graph Theory，Discrete Mathematics，Discrete Applied Mathematics等国际重要期刊发表多篇学术论文。