We prove that every 3-edge-connected graph G has a 3-flow ϕ with the property that $|\mathrm{supp}(\varphi )|\ge \frac{5}{6}|E(G)|$. The graph $K_4$ demonstrates that this $\frac{5}{6}$ ratio is best possible; there is an infinite family where $\frac{5}{6}$ is tight.

中文翻译：

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3流支持

我们证明每个3边连通图G都有一个3流ϕ，其性质为$|\mathrm{支持}（\varphi ）|\ge \frac{5}{6}|Ë（G）|$。图${ķ}_4$ 证明这 $\frac{5}{6}$比率最好 有一个无限的家庭$\frac{5}{6}$ 很紧