Nonorientable hamilton cycle embeddings of complete tripartite graphs

A cyclic construction is presented for building embeddings of the complete tripartite graph K-n,K-n,K-n on a nonorientable surface such that the boundary of every face is a hamilton cycle. This construction works for several families of values of n, and we extend the result to all n with some methods of Bouchet and others. The nonorientable genus of K-t,K-n,K-n,K-n for t >= 2n, is then determined using these embeddings and a surgical method called the 'diamond sum' technique. (C) 2012 Elsevier B.V. All rights reserved.