In this note, we consider triangulations of the plane. Ozeki and the second author asked whether there are non-hamiltonian 1-tough triangulations in which every two separating triangles are disjoint. We answer this question in the affirmative and strengthen a result of Nishizeki by proving that there are infinitely many non-hamiltonian 1-tough triangulations with pairwise disjoint separating triangles.
|Number of pages||4|
|Journal||Discrete Applied Mathematics|
|Publication status||Published - 2020 Sept 30|
- Separating triangle
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics