Non-hamiltonian 1-tough triangulations with disjoint separating triangles

Jun Fujisawa; Carol T. Zamfirescu

doi:10.1016/j.dam.2020.03.053

Non-hamiltonian 1-tough triangulations with disjoint separating triangles

Jun Fujisawa, Carol T. Zamfirescu

Faculty of Business and Commerce

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	622-625
Number of pages	4
Journal	Discrete Applied Mathematics
Volume	284
DOIs	https://doi.org/10.1016/j.dam.2020.03.053
Publication status	Published - 2020 Sept 30

Keywords

1-tough
Non-hamiltonian
Separating triangle
Triangulation

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2020.03.053

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title = "Non-hamiltonian 1-tough triangulations with disjoint separating triangles",

abstract = "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.",

keywords = "1-tough, Non-hamiltonian, Separating triangle, Triangulation",

author = "Jun Fujisawa and Zamfirescu, {Carol T.}",

note = "Funding Information: Fujisawa{\textquoteright}s work is supported by the Japan Society for the Promotion of Science , Grant-in-Aid for Scientific Research (B) 16H03952 and Grant-in-Aid for Scientific Research (C) 17K05349 . Zamfirescu{\textquoteright}s research is supported by a Postdoctoral Fellowship of the Research Foundation Flanders (FWO) . Publisher Copyright: {\textcopyright} 2020 Elsevier B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

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AU - Zamfirescu, Carol T.

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PY - 2020/9/30

Y1 - 2020/9/30

N2 - 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.

AB - 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.

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KW - Non-hamiltonian

KW - Separating triangle

KW - Triangulation

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Non-hamiltonian 1-tough triangulations with disjoint separating triangles

Abstract

Keywords

ASJC Scopus subject areas

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