报告主题：A Strengthening of Erdős-Gallai Theorem and Proof of Woodall’s Conjectureg (Erdős-Gallai定理的加强与Woodall猜想的证明)
时间：2021年1月6日19:00-22:00
地点：腾讯会议144 308 263
报告人：李斌龙(邀请人：张赞波)
报告摘要：For a 2-connected graph G on n vertices and two vertices x,y ∈ V (G), we prove that there is an (x,y)-path of length at least k if there are at least (n−1)/2 vertices in V(G)\{x,y} of degree at least k. This strengthens a well-known theorem due to Erdős and Gallai in 1959. As the first application of this result, we show that a 2-connected graph with n vertices contains a cycle of length at least 2k if it has at least n/2+k vertices of degree at least k. This confirms a 1975 conjecture made by Woodall. As other applications, we obtain some results which generalize previous theorems of Dirac, Erdős-Gallai, Bondy, and Fujisawa et al., present short proofs of the path case of Loebl-Komlós-Sós Conjecture which was verified by Bazgan et al. and of a conjecture of Bondy on longest cycles (for large graphs) which was confirmed by Fraisse and Fournier, and make progress on a conjecture of Bermond.
报告人简介：李斌龙，荷兰Twente大学博士，捷克West Bohemia大学博士后，丹麦技术大学访问学者，现为西北工业大学数学与统计学院副教授。主要从事图论研究工作，在图的Hamilton性等方面取得一系列研究成果。主持国家自然科学基金青年项目一项。在JCTB,J. Graph Theory, European J. Combinatorics等期刊发表论文50余篇。