The theory of matching in graphs concerns the problem of pairing up objects, subject to constraints on which
objects may be paired. It is a well developed theory that is not only of tremendous mathematical importance,
but is also widely applied to efficiently deal with allocation and scheduling problems. Much less in known,
however, about the equally important but harder problem of dividing objects into collections of three or more.
This project will address this deficiency by developing the theory of matching in important combinatorial
objects. The problems it will solve are of great significance in their own right, and when considered together
will help to lay a foundation for a more general theory of matching.