Non-hamiltonian triangulations with distant separating triangles

In 1996 Bohme, Harant, and Tkac 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, Bohme and Harant 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. (C) 2018 Elsevier B.V. All rights reserved.