We consider a planar graph $G$ in which the edges have nonnegative integer lengths such that the length of every cycle of $G$ is even, and three faces are distinguished, called holes in $G$. It is known that there exists a packing of cuts and (2,3)-metrics with nonnegative integer weights in $G$ which realizes the distances within each hole. We develop a purely combinatorial strongly polynomial-time algorithm to find such a packing.

中文翻译：

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在具有三个孔的平面图中填充切口和（2,3）度量的有效算法

我们考虑一个平面图 $G$ 其中边具有非负整数长度，使得每个循环的长度为 $G$甚至，三面区分，称为孔在$G$。已知存在一个带有非负整数权重的割和（2,3）度量的包装$G$实现每个孔内的距离。我们开发了一种纯粹的组合式强多项式时间算法来找到这种压缩。