Extremal Minimal Bipartite Matching Covered Graphs: A Complete Characterization
Every extremal minimal bipartite matching covered graph is obtained from two copies of a halin tree by adding a matching between the corresponding leaves.
Priority-Neutral Matchings Lack Key Structural Properties of Stable Matchings
Priority-neutral matchings, a generalization of stable matchings that allows for certain priority violations, lack crucial structural properties enjoyed by stable matchings, such as distributivity and representation via a partial order on rotations.
Symmetric Mechanisms for Matching Problems with Two Sides
The core message of this paper is to introduce a general notion of fairness for matching mechanisms, called symmetry, which encompasses different levels of fairness within and across the two sets of agents. The authors prove several possibility and impossibility results involving symmetry, stability, and resoluteness of matching mechanisms.
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