Nowhere-zero Flow and Group Connectivity of Graphs



报告题目:Nowhere-zero Flow and Group Connectivity of Graphs


报告摘要: As a generalization of map-coloring problems, Tutte initiated the study of  nowhere-zero flow of graphs in 1950s, and he proposed some intriguing flow conjectures which are still some of the major open problems in graph theory.  Jaeger and others further extended the integer flow theory to circular flows and group connectivity of graphs. In this talk, we will introduce some recent results on Tutte's flow conjectures and related topics. Some nice positive results on Tutte and Jaeger's conjectures are obtained recently by Thomassen(JCTB 2012) and Lovasz et al.(JCTB 2013). Inspired by this method,  we show that every 8-edge-connected graph has circular flow strictly less than 3, which approximates to the conjectured value 2.5 and provides evidence to Tutte's 5-Flow conjecture. On the other hand, we disprove Jaeger's circular flow conjecture and propose some new conjectures on circular flows.

报告时间: 20171127日(周一),下午400




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