报告题目：Tutte's integer flow conjectures
报告人：张存铨 教授 美国西弗吉尼亚大学
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邀请人: 朱强 教授
报告时间：2018年4月12日（周四）下午2:30-3:45
报告地点：南校区信远楼II206我院报告厅
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：
Let G be a graph with an orientation D. A mapping f from E(G) to { -1, 1, -2, 2, …, -(k-1), k-1 } is called a nowhere-zero k-flow if, for every vertex v in V(G), the flow in v and out v are equal.  The integer flow problem is a dual of the vertex coloring problem: it is pointed out by Tutte that a planar graph G admits a nowhere-zero k-flow if and only if G is k-face-colorable.
Tutte proposed several important  conjectures about integer flows, such as, 3-flow, 4-flow and 5-flow conjectures. Those conjectures, though there are some breakthrough in last 40 years, remain widely open.
This talk will introduce not only some history but alsosome basics of Tutte's flow theory.

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