References
- [1] D.W. Barnette, A. L. Edelson, All 2−manifolds have finitely many minimal triangulations, Israel J. Math. 67 (1989), 123-128.10.1007/BF02764905
- [2] G. Brinkmann, B. D McKay Fast generation of planar graphs, MATCH Commun. Math. Comput. Chem. 58(2) (2007), 323-357.
- [3] A. Boulch, É. Colin de Verdière, A. Nakamoto, Irreducible triangulations of surfaces with boundary, Graphs Comb., 29 No. 6 (2013), 1675–1688.10.1007/s00373-012-1244-1
- [4] M.J. Chávez, S. Lawrencenko, A. Quintero, M. T. Villar, Irreducible triangulations of the Möbius band, Bul. Acad. Sţiinţe Repub. Mold. Mat., No. 2(75) (2014), 44–50.
- [5] M.J. Chávez, S. Negami, A. Quintero, M. T. Villar, Generating families of surface triangulations. The case of punctured surfaces with inner degree at least 4. arXiv e-print service, Cornell University Library, http://arxiv.org/abs/1507.03975v2, (2015).
- [6] M.J. Chávez, S. Negami, A. Quintero, M. T. Villar, A generating theorem of punctured surface triangulations with inner degree at least 4. Math. Slovaca 69, No. 5 (2019), 969–978.10.1515/ms-2017-0281
- [7] D. Fernández-Ternero, E. Macías-Virgós, N. A. Scoville, J. A. Vilches Strong Discrete Morse Theory and Simplicial L-S Category: A Discrete Version of the Lusternik-Schnirelmann Theorem, Discret. Comput. Geom. 63 (2020), 607-623.10.1007/s00454-019-00116-8
- [8] J. Fujisawa, A. Nakamoto, K. Ozeki, Hamiltonian cycles in bipartite toroidal graphs with a partite set of degree four vertices, J. Combin. Theory, Ser. B 103 (2013), 46-60.10.1016/j.jctb.2012.08.004
- [9] B. Grunbaum, Polytopes, graphs, and complexes, Bull. Amer. Math. Soc. 76 (1970), 1131-1201.10.1090/S0002-9904-1970-12601-5
- [10] K. Kawarabayashi, K. Ozeki, 4-connected projective-planar graphs are Hamiltonian-connected, J. Combin. Theory Ser. B 112 (2015), 36-69.10.1016/j.jctb.2014.11.006
- [11] H. Komuro, A. Nakamoto, S. Negami, Diagonal flips in triangulations on closed surfaces whith minimum degree at least 4, J. Combin. Theory Ser. B 76 (1999), 68-92.10.1006/jctb.1998.1889
- [12] B. Krüger, K. Mecke, Genus dependence of the number of (non-) orientable surface triangulations, Phys. Rev. D 93 (2016), 085018 (6 pp).10.1103/PhysRevD.93.085018
- [13] S. Lawrencenko, T. Sulanke, M. T. Villar, L. V. Zgonnik, M. J. Chávez, J. R. Portillo. Irreducible triangulations of the once-punctured torus, Sibirskie Elektronnye Matematicheskie Izvestiya. Vol. 15 (2018), 277-304.
- [14] A. Malnič, R. Nedela, K-Minimal triangulations of surfaces, Acta Math. Univ. Comenianae 64, 1 (1995), 57-76.
- [15] N. Matsumoto, A. Nakamoto, Generating 4-connected even triangulations on the sphere, Discrete Math. 338 (2015), 64-70.10.1016/j.disc.2014.08.017
- [16] N. Matsumoto, A. Nakamoto, T. Yamaguchi, Generating even triangulations on the torus, Discrete Mathematics 341 (2018), 2035-2048.10.1016/j.disc.2018.04.002
- [17] A. Nakamoto, H. Motoaki, Generating 4-connected triangulations on closed surfaces, Mem. Osaka Kyoiku Univ. Ser. III Nat. Sci. Appl. Sci. 50, no. 2 (2002), 145-153.
- [18] A. Nakamoto, S. Negami, Generating triangulations on closed surfaces with minimum degree at least 4, Discrete Math. 244 (2002), 345-349.10.1016/S0012-365X(01)00093-0
- [19] S. Negami, Triangulations, Handbook of Graph Theory, Second Edition. J. L. Gross, J. Yellen and P. Zhang (Ed.) Chapman and Hall/CRC Press, 876-901, 2014.10.1201/b16132-52
- [20] M. Nishina, Y. Suzuki, A generating theorem of simple even triangulations with a finitizable set of reductions, Discrete Math., 340 (2017), 2604-2613.10.1016/j.disc.2017.06.018
- [21] T. Sulanke, Generating irreducible triangulations of surfaces, arXiv:math/0606687v1 [math.CO], (2006).
- [22] T. Sulanke, F. H. Lutz, Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds, Eur. J. Comb. 30 (2009), 1965-1979.10.1016/j.ejc.2008.12.016
- [23] R. Thomas, X. Yu, 4-connected projective planar graphs are Hamiltonian, J. Combin. Theory Ser. B 62 (1994), 114-132.10.1006/jctb.1994.1058
- [24] H. Whitney, A theorem on graphs, Ann. Math. 32 (1931), 378-390.10.2307/1968197