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Hamiltonicity of 5-connected toroidal triangulations. (English) Zbl 0841.05061
The authors prove that each 5-connected toroidal triangulation has a contractible Hamiltonian cycle.

MSC:
05C45 Eulerian and Hamiltonian graphs
05C10 Planar graphs; geometric and topological aspects of graph theory
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[1] Barnette, Discrete Math. 70 pp 1– (1988)
[2] and , Graph Theory with Applications, North-Holland, New York (1976). · Zbl 1226.05083
[3] Chibi, J. Graph Theory 10 pp 449– (1985)
[4] and , Planar Graphs: Theory and Algorithms, North-Holland, Amsterdam (1988).
[5] and , Planar and toroidal graphs with homeomorphically irreducible spanning trees, prepring. · Zbl 0843.05025
[6] Grünbaum, Bull. Amer. Math. Soc. 76 pp 1131– (1970)
[7] Graph Theory, Addison-Wesley, Reading, MA (1972).
[8] Hocroft, SIAM J. Comput. 3 pp 135– (1973)
[9] Unexplored and semi-explored territories in graph theory, in New Directions in Graph Tehroy (ed.), Academic Press, New York (1973). · Zbl 0263.05101
[10] and , Representativity of surface embeddings, in Paths, Flows and VLSI-Layouts (, , and , eds.), Springer-Verlag, Berlin (1990), pp. 293–328. · Zbl 0735.05032
[11] Thomas, J. Combin. Theory Ser. B 62 pp 114– (1994)
[12] personal communication.
[13] Thomassen, J. Graph Theory 7 pp 169– (1983)
[14] Thomassen, J. Combin. Theory Ser. B 48 pp 155– (1990)
[15] Tutte, Trans. Amer. Math. Soc. 82 pp 99– (1956)
[16] Graph Theory, Cambridge University Press, Cambridge (1984).
[17] Whtney, Ann. Math. 32 pp 378– (1931)
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