We show that given a SM instance G as input we can find a largest collection of pairwise edge-disjoint stable matchings of G in time linear in the input size. This extends two classical results: 1. The Gale-Shapley algorithm, which can find at most two ("extreme") pairwise edge-disjoint stable matchings of G in linear time, and 2. The polynomial-time algorithm for finding a largest collection of pairwise edge-disjoint perfect matchings (without the stability requirement) in a bipartite graph, obtained by combining K\"{o}nig's characterization with Tutte's f-factor algorithm.

中文翻译：

---

线性时间中不相交的稳定匹配

我们表明，给定一个SM实例G作为输入，我们可以在输入大小的时间线性范围内找到G的成对边不相交稳定匹配的最大集合。这扩展了两个经典结果：1. Gale-Shapley算法，它最多可以在线性时间内找到G的两个（“极端”）成对边不相交的稳定匹配，以及2.用于找到最大集合的多项式时间算法通过将Kn“ nig的特征与Tutte的f因子算法相结合获得的二部图中成对的边不相交的完美匹配（无稳定性要求）。