Hamilton cycles in plane triangulations

We extend Whitney’s Theorem that every plane triangulation without separating triangles is hamiltonian by allowing some separating triangles. More precisely we define a decomposition of a plane triangulation G into 4-connected ‘pieces’ and show that if each piece shares a triangle with at most three other pieces then G is hamiltonian. We provide an example to show that our hypothesis that ‘each piece shares a triangle with at most three other pieces’ cannot be weakened to ‘four other pieces’. As part of our proof we also obtain new results on Tutte cycles through specified vertices in planar graphs. ∗Partially supported by NSF grants DMS–9531824 and 9970527