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 P² 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 P² 3-manifolds that can be formed from at most 10 tetrahedra.