报告人：李佳傲 博士 南开大学

时间：12月12号 10：30-11：30

地点：五教5401

摘要：

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.