学术海报

11月19日 张存铨教授学术报告(数学与统计学院)

发布者:周郑坤发布时间:2018-11-15浏览次数:495

报 告 人:张存铨 教授

报告题目:Integer flows in Cayley graphs

报告时间:2018年11月19日(周一)下午14:00

报告地点:静远楼1506报告厅

主办单位:数学与统计学院、科学技术研究院

报告人简介:

  美国西弗吉尼亚大学数学系教授、博士生导师、eberly杰出教授,主要研究领域为图论和组合数学、离散优化和生物信息学,是享誉盛名的国际图论专家。张存铨教授1986年从加拿大著名的西蒙菲莎大学获得博士学位,1989年以优异的科研成果被破格提前提升为终身副教授。1996年提升为正教授。他曾独立获得八个美国科技基金会等科研基金,是联邦定期资助的唯一主要研究者,屡次获得校方的最佳科研奖。在《Journal of Combinatorial Theory B》、 《Journal of Graph Theory》等国际著名期刊上发表论文一百余篇。他的专著 《Integer Flows and Cycle Covers of Graphs》 和 《Circuit Double Covers of Graphs》在同行中享有极高的评价。

报告摘要:

  This is a survey talk about Tutte's integer flows in Cayley graphs.

  Alspach conjectured that every connected Cayley graph contains a Hamilton cycle. After almost five decades, Alspach's conjecture remains widelyopen. Note that every Hamiltonian graph admits a nowhere-zero 4-flow.The following is a weaker version of Alspach's conjecture (by Alspach,Liu and Z) that every Cayley graph admits a nowhere-zero 4-flow (equivalently, there is no Cayley snarks). Integer flow theory was introducedby Tutte as a dual version of graph coloring. Tutte proposed several conjectures about integer flows, such as, 3-, 4- and 5-flow conjecture. Theprogress of Tutte's conjectures for Cayley graphs will be surveyed andpossible strengthening of those early results will be discussed based onsome recent progress in flow theory.