Regular orientable imbeddings of complete graphs

Enumerating the orientable 2-cell imbeddings of complete bipartite graphs

Orientable Step Domination of Complete r-Partite Graphs

This paper provides lower orientable k-step domination number and upper orientable k-step domination number of complete r-partite graph for 1 ≤ k ≤ 2. It also proves that the intermediate value theorem holds for the complete r-partite graphs.

Triangulations of orientable surfaces by complete tripartite graphs

Orientable triangular embeddings of the complete tripartite graph Kn,n,n correspond to biembeddings of Latin squares. We show that if n is prime there are at least e ln n−n(1+o(1)) nonisomorphic biembeddings of cyclic Latin squares of order n. If n = kp, where p is a large prime number, then the number of nonisomorphic biembeddings of cyclic Latin squares of order n is at least e ln p−p(1+ln . ...

The orientable genus of certain complete tripartite graphs

In 1969, White conjectured that the orientable genus of the complete tripartite graph Kl,m,n, with l ≥ m ≥ n, is ⌈ (l−2)(m+n−2) 4 ⌉ . In this talk we describe progress on this conjecture. We can show that White’s conjecture is true in the cases where (m, n), reduced modulo 4, is (0, 0), (0, 2), (1, 1), (2, 0), (2, 1), (2, 2), (2, 3) or (3, 3). We discuss similarities and differences between our...

The orientable genus of some joins of complete graphs with large edgeless graphs

In an earlier paper the authors showed that with one exception the nonorientable genus of the graph Km +Kn with m ≥ n−1, the join of a complete graph with a large edgeless graph, is the same as the nonorientable genus of the spanning subgraph Km+Kn = Km,n. The orientable genus problem for Km +Kn with m ≥ n−1 seems to be more difficult, but in this paper we find the orientable genus of some of t...