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Face pairing graphs and 3-manifold enumeration

Benjamin A. Burton
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Abstract

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.

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Benjamin A. Burton. 2003-11-20. Face pairing graphs and 3-manifold enumeration. https://doi.org/10.1142/s0218216504003627

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