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 2   an   2 − o ( n   2) non‐isomorphic face 2‐colourable triangulations of K n and K n,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