Enumeration of non-orientable 3-manifolds using face pairing graphs and union-find
<|reference_start|>Enumeration of non-orientable 3-manifolds using face pairing graphs and union-find: Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing graphs, and pruning techniques are improved using a modification of the union-find algorithm. Using these results we catalogue all 136 closed non-orientable P^2-irreducible 3-manifolds that can be formed from at most ten tetrahedra.<|reference_end|>
@article{burton2006enumeration,
    title={Enumeration of non-orientable 3-manifolds using face pairing graphs and
  union-find},
    author={Benjamin A. Burton},
    journal={Discrete and Computational Geometry 38 (2007), no. 3, 527-571},
    year={2006},
    doi={10.1007/s00454-007-1307-x},
    archivePrefix={arXiv},
    eprint={math/0604584},
    primaryClass={math.GT cs.CG math.CO}
}