Non-bipartite matching problems arise naturally in many multi-agent systems, yet they face a fundamental challenge absent from classical bipartite markets: even under strict preferences, stable matchings need not exist. This non-existence requires a careful combinatorial study of preference structures, and calls for the design of advanced algorithms when aiming for alternative fairness or relaxed stability guarantees in such settings. I study the structural origins of instability in non-bipartite preference systems, develop new optimality criteria inspired by both classical social choice theory and by real-world requirements, and design efficient algorithms for the computation of matchings satisfying such criteria if possible.
Frederik Glitzner (Sun,) studied this question.