This project concerns the isomorphism problem for combinatorial objects. This is the problem of determining the complexity of deciding if two objects are isomorphic. In the case of graphs, this problem, although not NP-complete, is considered NP-hard. A combinatorial object is a finite set called the vertices, and certain other sets associated with that finite set. Combinatorial objects include graphs, designs, simplicial complexes, directed graphs, and partially ordered sets. An isomorphism between two combinatorial objects is a one-to-one correspondence between the two vertex sets that preserves the structure given by the associated sets.
