%0 Journal Article
%T Face pairing graphs and 3-manifold enumeration
%A Benjamin A. Burton
%J Mathematics
%D 2003
%I arXiv
%R 10.1142/S0218216504003627
%X The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph. These results are then applied to the enumeration of closed minimal P^2-irreducible 3-manifold triangulations, leading to a significant improvement in the performance of the enumeration algorithm. Results are offered for both orientable and non-orientable triangulations.
%U http://arxiv.org/abs/math/0307382v3