ORIENTABLE AND NONORIENTABLE GENERA FOR SOME COMPLETE TRIPARTITE GRAPHS

摘要

In this paper, we obtain three general reduction formulas to determine the orientable and nonorientable genera for complete tripartite graphs. As corollaries, we (1) reduce the determination of the orientable (nonorientable, respectively) genera of 75 percent (85 percent, respectively) of nonsymmetric (with respect to l, m, and n) K_(l,m,n) to that of K_(m,m,n), and (2) determine the orientable and nonorientable genera for several classes of complete tripartite graphs.