# Disjoint Stable Matchings in Linear Time

@inproceedings{Nimbhorkar2020DisjointSM, title={Disjoint Stable Matchings in Linear Time}, author={Prajakta Nimbhorkar and Geevarghese Philip and Vishwa Prakash HV}, booktitle={International Workshop on Graph-Theoretic Concepts in Computer Science}, year={2020} }

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…

## One Citation

### Diverse Non Crossing Matchings*

- Mathematics
- 2022

A perfect matching M on a set P of n points is a collection of line segments with endpoints from P such that every point belongs to exactly one segment. A matching is non-crossing if the line…

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