Stable matchings and stable partitions

Recently Tan [7] defined a new structure for the stable roommates problem, called a “stable partition” which is a generalization of the notion of the stable matching. He proved that every instance of that problem contains at least one such structure, and obtained a succinct certificate of the non-existence of a stable matching. In this paper. we establish several results on properties of the stable partitions, present a simple proof of a recent theorem of Tan, and solve a maximum stable matching problem.