Non-hamiltonian 1-tough triangulations with disjoint separating triangles

Jun Fujisawa, Carol T. Zamfirescu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)622-625
Number of pages4
JournalDiscrete Applied Mathematics
Publication statusPublished - 2020 Sept 30


  • 1-tough
  • Non-hamiltonian
  • Separating triangle
  • Triangulation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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