Department of Mathematics，West Virginia University
报告题目：Flows of signed graphs
报告摘要：Converting modulo flows into integer-valued flows is one of the most critical steps in the study of integer flows. Tutte and Jaeger's pioneering work shows the equivalence of modulo flows and integer-valued flows for ordinary graphs.
However, such equivalence does not hold any more for signed graphs. This motivates us to study how to convert modulo flows into integer-valued flows for signed graphs. We generalize some early results by Xu and Zhang (Discrete Math.299, 2005), Schubert and Steffen (European J. Combin.48, 2015), and Zhu (J. Combin. Theory Ser. B 112, 2015),and show that, for signed graphs, every modulo (2+1/p)-flow, where p is positive integer or infinity, can be converted/extended into an integer-valued flow.
In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph has a nowhere-zero 6-flow.The best published result is Zyka's 30-flow and was recently improved to 12-flow by DeVos. As an application of our aforementioned results, we further strengthen DeVos' result for bridgeless signed graphs, and show that every bridgeless flow-admissible signed graph admits a nowhere-zero 11-flow.We also verifiy Bouchet's conjecture for signed graphs without edge-disjoint unbalanced circuits.
报告人简介：罗荣， 1996年本科毕业于中国科技大学， 1998年硕士毕业于中国科技大学， 2002年博士毕业于西弗吉尼亚大学， 2002-2012，任职于Middle Tennessee State University, 现为西弗吉尼亚数学系教授。 主要研究方向是图的染色以及相关课题， 在Vizing关于边染色的四个猜想取得一系列突破性进展， 并在整数流和群连通度上取得一系列突出结果。