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Non-Hamiltonian triangulations with distant separating triangles. (English) Zbl 1387.05141
Summary: T. Böhme et al. [Tatra Mt. Math. Publ. 9, 97–102 (1996; Zbl 0857.05065)] asked whether there exists a non-Hamiltonian triangulation with the property that any two of its separating triangles lie at distance at least 1. Two years later, T. Böhme and J. Harant [Discrete Math. 191, No. 1–3, 25–30 (1998; Zbl 0958.05085)] answered this in the affirmative, showing that for any non-negative integer $$d$$ there exists a non-hamiltonian triangulation with seven separating triangles every two of which lie at distance at least $$d$$. In this note we prove that the result holds if we replace seven with six, remarking that no non-hamiltonian triangulation with fewer than six separating triangles is known.

##### MSC:
 05C45 Eulerian and Hamiltonian graphs
##### Keywords:
triangulation; separating triangle; non-Hamiltonian
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##### References:
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