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On Hamiltonian cycles in 4- and 5-connected plane triangulations

✍ Scribed by Thomas Böhme; Jochen Harant


Book ID
108316259
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
311 KB
Volume
191
Category
Article
ISSN
0012-365X

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✍ Jan Kratochvil; Dainis Zeps 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 185 KB 👁 2 views

It is proved that if a planar triangulation different from K3 and K4 contains a Hamiltonian cycle, then it contains at least four of them. Together with the result of Hakimi, Schmeichel, and Thomassen [21, this yields that, for n 2 12, the minimum number of Hamiltonian cycles in a Hamiltonian planar

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The triangulations of the torus can be generated from a set of 21 minimal triangulations by vertex splitting. We show that if we never create a 3-valent vertex when we split them we generate the 4-connected triangulations. In addition if we never create two adjacent 4-valent vertexes then we gener