报告题目：Flows of graphs (signed and unsigned)

报告简介：In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. The name ``signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1955.

Nowhere-zero flows in unsigned graphs were introduced by Tutte in 1954 as a dual problem to vertex-coloring of (unsigned) planar graphs. Tutte shows that the famous map 4-color conjecture (now known as the 4-color theorem) is equivalent to the statement that every bridgeless planar graph admits a nowhere-zero 4-flow. In general, Seymour shows that every bridgeless graph admits a nowhere-zero 6-flow. Tutte's 5-flow conjecture indicates that the flow value 6 in Seymour's theorem may not be the best possible and 5 would be the best possible. The definition of nowhere-zero flows on signed graphs naturally comes from the study of embeddings of graphs in non-orientable surfaces, where nowhere-zero flows emerge as the dual notion to local tensions. Bouchet started to study it systematically in 1983. He also stated a conjecture that parallels to Tutte's 5-Flow Conjecture and occupies a similarly central place in the area of signed graphs. He conjectured that Every flow-admissible signed graph admits a nowhere-zero 6-flow.

In this talk, I will give an introduction to flows of unsigned graphs and signed graph and present some progresses toward Bouchet’s 6-flow conjecture. In particular I will explain the significant difference of integer flows between unsigned graphs and signed graphs.

报告人：罗荣教授，美国西弗吉尼亚大学

报告时间：2019年06月05日（星期三）下午 3:30

报告地点：扬州大学瘦西湖校区数学科学学院38号楼103报告厅

主办单位：扬州大学数学科学学院

欢迎广大师生参加！