Mike J. Grannell

Exponential Families of Non-Isomorphic Triangulations of Complete Graphs

We prove that the number of non-isomorphic face 2-colourable triangulations of the complete graph Kn in an orientable surface is at least 2n2/54?O(n) for n congruent to 7 or 19 modulo 36, and is at least 22n2/81?O(n) for n congruent to 19 or 55 modulo 108.

The Resolution of the Anti-Pasch Conjecture

We show that an anti-Pasch Steiner triple system of order

Construction techniques for anti-pasch steiner triple systems

v

Biembeddings of Latin squares and Hamiltonian decompositions

exists for

Face 2-Colourable Triangular Embeddings of Complete Graphs

v\equiv 1

Surface embeddings of Steiner triple systems

or 3 (mod 6), apart from

On 6-sparse Steiner triple systems

v=7

Designs and topology

and 13.

Nonorientable biembeddings of Steiner triple systems

Four methods for constructing anti-Pasch Steiner triple systems are developed. The first generalises a construction of Stinson and Wei to obtain a general singular direct product construction. The second generalises the Bose construction. The third employs a construction due to Lu. The fourth employs Wilson-type inflation techniques using Latin squares having no subsquares of order two. As a consequence of these constructions we are able to produce anti-Pasch systems of order

Some new perfect Steiner triple systems

v