潍坊学院 蔡建生教授、山东师范大学 张霞教授 学术报告

报告题目1：Some Results on Second Neighborhood Conjucture in Digraph

报告人：蔡建生教授，潍坊学院

报告时间：2024年10月22日（周二）18:30-19:30

会议地点：腾讯会议：970-348-982

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，潍坊学院数学与统计学院教授，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。

报告题目2：The chromatic indices of hypergraphs

报告人：张霞教授，山东师范大学

报告时间：2024年10月22日（周二）19:30-20:30

会议地点：腾讯会议：970-348-982

摘要：The chromatic index of a hypergraph $H$ is the minimum number of colors needed to color the edges of $H$ such that any two intersecting edges receive distinct colors. Let $D(H)$ denote the maximum strong degree of $H$. In 1980s, Berge and Meyniel, independently, conjectured that the chromatic index of every loopless linear hypergraph $H$ is no more than $(D(H)+1)$, which implies the Erd\H{o}s-Faber-Lov\'asz conjecture. In 2000, Dvo\v{r}\'ak generalized Shannon’s result to hypergraphs without multiple 2-edges and conjectured that the chromatic index of every loopless hypergraph $H$ is at most $\lfloor1.5D(H)\rfloor$.

Recently, we confirm the Berge-Meyniel conjecture for two classes of linear hypergraphs, and verify the Dvo\v{r}\'ak's conjecture for weakly 2-edge-sparse hypergraphs and hypergraphs without intersecting multiple 2-edges. The above results strictly extend several related results due to Bretto, Faisant and Hennecart (Discrete Math. 2020), Alesandroni (Discrete Math. 2021), Dvo\v{r}\'ak (Eur. J. Comb. 2000), respectively.

报告人简介：张霞，本科、博士就读于山东大学数学学院，2007年获理学博士学位。现为山东师范大学数学与统计学院教授、博士生导师，校级科研创新团队“图论组合优化创新团队”负责人，山东师范大学东岳学者拔尖人才。研究领域为图论及其应用，先后主持3项国家自然科学基金、3项省自然科学基金。作为访问学者先后访问中国科学院数学与系统科学研究院、加拿大维多利亚大学、美国威廉玛丽学院。现任中国运筹学会理事、中国运筹学会图论组合分会理事、中国工业与应用数学学会ICT领域的数学专委会委员。