12-12【李佳傲】五教5401 吴文俊数学重点实验室组合图论系列讲座之150

Tutte's and Jaeger's flow conjectures predict existence of flows for highly connected graphs. Seymour and Jaeger provided $6$-flows and $4$-flows for $2$- and $4$-edge-connected graphs, respectively.  Lovasz, Thomassen, Wu and Zhang  showed that every $6p$-edge-connected graph admits a circular $(2+\frac{1}{p})$-flow. In this talk, we are able to provide a  flow value for each given  edge connectivity, showing that  every $(6p-2)$-edge-connected graph admits a circular $(2+\frac{2}{2p-1})$-flow, and every $(6p+2)$-edge-connected admits a circular flow strictly less than $2+\frac{1}{p}$. Similar results on flows of signed graphs under given edge connectivity are discussed.