报告题目：Jaeger conjecture, integer flow and modular orientation

报告人：张存铨，教授，西弗吉尼亚大学

邀请人：刘三阳教授，朱强副教授

报告时间：2017年4月12日下午2:30

报告地点：信远楼II206数统院报告厅

报告人简介：张存铨 (Cun-Quan Zhang)，博士，美国West Virginia大学 Eberly首席教授，Discrete Mathematics, Algorithms and Applications和Advances and Applications in Discrete Mathematics 编委，国际上从事图论及其应用研究的著名专家。具体研究工作包括：图论理论方面的流理论、圈覆盖问题；图论应用方面的网络结构、离散优化、算法、优化、数据挖掘、社会网络以及生物信息学等。先后主持美国国家级科研项目11项，出版两本专著 《Integer Flows and Cycle Covers of Graphs》 和 《Circuit Double Covers of Graphs》，仅国际顶级期刊Transaction of the American Mathematics Society、Journal of Combinatorial Theory B、Journal of Graph Theory上发表的论文就有40余篇

报告摘要：Jaeger conjectured that every 4p-edge-connected graph admits a modulo (2p+1)-orientation. Note that for p=1,2, Jaeger`s conjecture implies the famous 3-flow and 5-flow conjectures of Tutte. Jaeger`s conjecture was partially proved by Lovàsz et al. (JCTB 2013) for 6p-edge-connected graphs.

In this talk, we show the existence of infinite families of counterexamples to Jaeger`s conjecture.

For p≥3, there are 4p-edge-connected graphs not admitting modulo (2p+1)-orientation; for p≥5, there are (4p+1)-edge-connected graphs not admitting modulo (2p+1)-orientation.

(Collaboration with Miaomiao Han, Jiaao Li, Yezhou Wu.)