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Generating the 4-connected and strongly 4-connected triangulations on the torus and projective plane

✍ Scribed by D.W. Barnette

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
978 KB
Volume
85
Category
Article
ISSN
0012-365X

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✦ Synopsis

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 generate the strongly 4-connected triangulations.

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## Abstract We prove that all 3‐connected 4‐regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all con