报告题目：Integer Flow and Circular Flow of Graphs
报告人：Jiaao Li (West Virginia University)
摘要： A flow in a directed graph is a map from the edge set to real numbers satisfying Kirchhoff law. That is, for every vertex, the sum of the flows entering it equals to the sum of the flows exiting it. The concept of integer flow was introduced by Tutte as a generalization of map-colouring problems. Circular Flow is a further refinement of integer flows. For a rational number $r\geq 2$, an undirected graph $G$ admits a circular $r$-flow if there is an orientation $D$ of $G$ and a function $f\mapsto [1, r-1]$ such that $(D, f)$ forms a flow. Jaeger(1981) conjectured that every $4p$-edge-connected graph admits a circular $(2+1/p)$-flow, which is related to Tutte's Flow Conjectures. It is proved by Lovasz-Thomassen-Wu-Zhang in 2013 that every $6p$-edge-connected graph admits a circular $(2+1/p)$-flow. In this talk, we discuss some new results and suggest several new problems on Jaeger's conjecture and related topics.