报告人： 张存铨
报告题目： Nowhere-zero $3$-Flows in Graphs and Signed Graphs
报告时间： 2014年10月23日（周四）下午2点
报告地点： 静远楼1506学术报告厅
报告摘要： Tutteobserved that every nowhere-zero $k$-flow on a plane graph gives rise to a k-vertex-coloring of its dual, and vice versa. Thus nowhere-zero integer flow and graph coloring can be viewed as dual concepts.Jaeger further shows that if a graph $G$ has a face-$k$-colorable $2$-cellembedding in some orientable surface, then it has a nowhere-zero k-flow.However,if the surface is non-orientable, then a face-k-coloring corresponds to a nowhere-zero k-flow in a signed graph arising from G. Graphs embedded in orientable surfaces are therefore a special case that the corresponding signs are all positive. In this talk, we present two recent results about integer flows for graphs and signed graphs.
(1) Tutteconjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. Extended from a recent breakthrough by Thomassen (JCTB 2012) that every 8-edge-connected graphs admits a nowhere-zero 3-flow, it is further proved that every 6-edge-connected graph admits a nowhere-zero 3-flow. (Joint work withLov\'asz, Thomassen and Y.Z. Wu).
(2) By applying the above result for graphs, Zhu proved that every 11-edge - connected signed graph admits a nowhere-zero 3-flow. This result is further improved for 8-edge-connected signed graphs. (Joint work with Y.Z. Wu, D. Ye and W. Zang.)
张存铨教授简介：
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。张存铨教授已有一百余篇论文，其中在SCI 2区上发表论文10余篇，SCI 3区上发表论文10余篇；他的经典专著《Integer Flows and Cycle Covers of Graphs》在同行中享有极高的评价。