Recursive constructions for triangulations

Three recursive constructions are presented; two deal with embeddings of complete graphs and one with embeddings of complete tripartite graphs. All three facilitate the construction of 2an2-o(n2) non-isomorphic face 2-colourable triangulations of Kn and Kn,n,n in orientable and non-orientable surfaces for values of n lying in certain residue classes and for appropriate constants a. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 87–107, 2002