报告题目1：5-cycle double cover and the shortest cycle cover of a bridgeless graph
报告时间：2024年10月10日（周四）18:30-19:30
报告地点：腾讯会议：653-688-085
报告摘要：It is conjectured that every bridgeless graph $G$ has a family $\mathcal{F}$ of even subgraphs such that each edge of $G$ is contained in precisely two members of $\mathcal{F}$ (say CDC), a stronger conjecture says that every bridgeless graph has a 5-even subgraph double cover (say 5-CDC) and the SCC conjecture that every bridgeless graph has an even subgraph cover with total length at most $\frac{21}{15}|E|$. In this talk, we first introduce a new approach related to nowhere-zero $4$-flows to attack these two conjectures, and then apply it together with Catlin reduction to present a sufficient condition for a superposition to have a 5-CDC. Finaly, we present a close relationship between the 4-even subgraph cover and the SCC conjecture.
报告人简介：郝荣霞，北京交通大学教授，博士生导师。主要从事图论和网络的研究，在IEEE TC、IEEE TPDS、Inform. Sci.、European J. Combin.、J. Graph Theory、SIAM J. Discrete Math.等国内外学术期刊上发表论文100余篇。主持和参加国家自然科学基金面上项目多项，其中参加国家自然科学基金重点项目两项。第八届国际华人数学家大会做45分钟邀请报告。曾获北京市高等教育教学成果一等奖、北京运筹学会青年优秀论文一等奖、北京交通大学“巾帼十杰”、“毕业生我最敬爱的教师”、“教学名师”和“智瑾奖教金优秀教师奖”等奖项，主编教材两本。中国运筹学会图论组合分会理事。CSIAM 信息通信数学及应用专委会委员，国际期刊International Journal of Computer Mathematics: Computer Systems Theory编委。
报告题目2：The generating set method and it's applications
报告时间：2024年10月10日（周四）19:30-20:30
报告地点：腾讯会议：653-688-085
报告摘要：Let $n$ and $k$ be two positive integers satisfying $n\geq 2k$. Let ${\mathcal A}$ be an intersecting family of ${[n] \choose k}$. The Erd\H{o}s-Ko-Rado Theorem states that $$|{\mathcal A}| \leq {n-1 \choose k - 1}.$$ There are many generalizations of this theorem and many ways to study it have been generated as well. The generating set method, which has so far not received much attention, is a very efficient way of them. In this talk, we will introduces this method and give some of its applications.
报告人简介：张华军，男，绍兴文理学院教授，浙江省高校中青年学科带头人，中国组合数学与图论专业委员会委员。2007年1月毕业于大连理工大学获博士学位，主要从事组合极值理论研究，解决了该领域中的一些公开问题和猜想，在J. Combin.Theory Ser. A、J. Combin.Theory Ser. B、J.Graph Theory和SIAM J. Discrete Math.等杂志上发表论文20余篇，主持或完成多项国家自然科学基金。