Hamiltonian-connectedness of triangulations with few separating triangles

Authors

DOI:

https://doi.org/10.11575/cdm.v14i1.62582

Keywords:

triangulation, maximal planar graph, hamiltonian-connected, decomposition tree

Abstract

We prove that 3-connected plane triangulations containing a single edge contained in all separating triangles are hamiltonian-connected. As a direct corollary we have that 3-connected plane triangulations with at most one separating triangle are hamiltonian-connected. In order to show bounds on the strongest form of this theorem, we proved that for any s >= 4 there are 3-connected triangulation with s separating triangles that are not hamiltonian-connected. We also present computational results which show that all `small' 3-connected triangulations with at most 3 separating triangles are hamiltonian-connected.

References

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Published

2019-12-25

Issue

Vol. 14 No. 1 (2019)

Section

Articles

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