Exponentially many nonisomorphic orientable triangular embeddings of K12s+3

It was proved earlier that there are constants M, c > 0 such that for every n M (resp., every n M , n / ≡ 0, 3mod 12) there are at least c2n/6 nonisomorphic nonorientable (resp., orientable) genus embeddings ofKn. In the present paper we show that for s 6 there are at least 2s−6 nonisomorphic OT-embeddings of K12s . As a byproduct, we give a relatively simple method of constructing index four current graphs with current group Z12s generating orientable triangular embeddings of K12s . © 2007 Elsevier B.V. All rights reserved.