勷勤数学•领军学者报告

题      目：Integral Flows on Graphs and Signed Graphs

报  告  人：范更华 教授  (邀请人：周波)

                                              福州大学

时      间：5月6日  16：00-17：30

地     点：数科院东楼401

报告人简介:

          福州大学教授，离散数学及其应用教育部重点实验室主任。国际图论界权威刊物《图论杂志》(Journal of Graph Theory)执行主编(Managing Editor)。主要从事图论领域中的结构图论、极图理论、带权图、欧拉图、整数流理论、子图覆盖等方向的基础理论研究，及图论在大规模集成电路设计中的应用。关于哈密顿圈存在性的成果以“范定理”、“范条件”被广泛引用而出现于多种国际学术刊物。一些成果作为定理出现在国外的教科书中。获1998年度国家杰出青年科学基金资助，获2005年度国家自然科学奖二等奖（独立完成人），曾任福州大学副校长、中国数学会组合数学与图论专业委员会主任、全国组合数学与图论研究会理事长、中国运筹学会副理事长、福建省数学学会理事长等。

摘      要：

A signed graph G is a graph associated with a mapping \sigma: E(G)\to \{+1,-1\}. Let G be a graph/signed graph with an orientation on each edge and let A be an abelian group. A function f, from the edge set E(G) of G to the nonzero elements of A, is call an A-flow of G if at each vertex v\in V(G), the sum of f(e) over  every e with head v is equal to the sum of f(e) over every e with tail v. Tutte conjectured that if a graph has a Z-flow, then it has a Z-flow f such that |f(e)|\leq 4 for each e\in E(G), which is related to graphs embedded in orientable surfaces. Bouchet conjectured that if a signed graph has a Z-flow, then it has a Z-flow f such tat |f(e)|\leq 5 for each e\in E(G), which is related to graphs embedded in nonorientable surfaces. The theory of flows has a strong connection with the coloring of graphs. In this talk, we focus on recent results on flows of signed graphs.

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