We show that for every ℓ, there exists $d_{\ell }$ such that every 3-edge-connected graph with minimum degree $d_{\ell }$ can be edge-partitioned into paths of length ℓ (provided that its number of edges is divisible by ℓ). This improves a result asserting that 24-edge-connectivity and high minimum degree provides such a partition. This is best possible as 3-edge-connectivity cannot be replaced by 2-edge connectivity.

中文翻译：

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将 3 边连通图边划分为路径

我们证明对于每个ℓ，存在$d_{\ell }$使得每个具有最小度数的 3 边连通图$d_{\ell }$可以边划分为长度为ℓ的路径（前提是它的边数可以被ℓ整除）。这改进了断言 24 边连通性和高最小度提供了这样一个分区的结果。这是最好的，因为 3 边缘连接不能被 2 边缘连接取代。