TL;DR
This paper establishes a precise condition for the existence of saturating stable matchings in bipartite graphs, and extends the analysis to perfect stable matchings, enhancing understanding of stable matching structures.
Contribution
It provides a necessary and sufficient condition for saturating stable matchings and extends the analysis to perfect stable matchings in bipartite graphs.
Findings
Characterization of conditions for saturating stable matchings
Extension of conditions to perfect stable matchings
Theoretical framework linking bipartite matchings to stability
Abstract
I relate bipartite graph matchings to stable matchings. I prove a necessary and sufficient condition for the existence of a saturating stable matching, where every agent on one side is matched, for all possible preferences. I extend my analysis to perfect stable matchings, where every agent on both sides is matched.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.