On the maximum genus of a graph

Abstract We define the maximum genus, γM(G), of a connected graph G to be the largest genus γ(N) for compact orientable 2-manifolds N in which G has a 2-cell imbedding. Several general results are established concerning the parameter γM(G), and the maximum genus of the complete graph Kn with n vertices is determined: γ M (K n ) = (n − 1)(n − 2) 4