A cyclic construction is presented for building embeddings of the complete tripartite graph K n,n,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,n,n,n ,… (More)
A distinguishing partition for an action of a group Γ on a set X is a partition of X that is preserved by no nontrivial element of Γ. As a special case, a distinguishing partition of a graph is a partition of the vertex set that is preserved by no nontrivial automorphism. In this paper we provide a link between distinguishing partitions of complete… (More)
It is shown that for v ≡ 1 or 3 (mod 6), every pair of Heffter difference sets modulo v gives rise to a biembedding of two 2-rotational Steiner triple systems of order 2v + 1 in a nonorientable surface.
In an earlier paper the authors constructed a hamilton cycle embedding of Kn,n,n in a nonori-entable surface for all n ≥ 1 and then used these embeddings to determine the genus of some large families of graphs. In this two-part series, we extend those results to orientable surfaces for all n = 2. In part II, a voltage graph construction is presented for… (More)