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@article{Motwani1989ExpandingGA, title={Expanding Graphs and the Average-case Analysis of Algorithms for Matchings and Related Problems}, author={Rajeev Motwani}, journal={J. ACM}, year={1989}, volume={41}, pages={1329-1356} }

- Published 1989 in STOC
DOI:10.1145/73007.73060

Hall's Theorem states that a bipartite graph has a perfect matching if and only if every set of vertices has an equal number of neighbours. Equivalently, it states that every non-maximum matching has an augmenting path if the graph is an expander with expansion 1. We use this insight to demonstrate that if a graph is an expander with expansion more than one than every non-maximum matching has a short augmenting path and, therefore, the bipartite matching algorithm performs much better on such… CONTINUE READING

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