Generating 4-connected even triangulations on the sphere

Generating 4-connected even triangulations on the sphere

In this paper, we prove that every 4-connected even triangulation on the sphere can be obtained from the octahedron by a sequence of two kinds of transformations called a 4-splitting and a twin-splitting, only through 4-connected even triangulations. As a corollary, taking a dual, we can also genera...

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Veröffentlicht in:Discrete mathematics 2015-01, Vol.338 (1), p.64-70
Hauptverfasser: Matsumoto, Naoki, Nakamoto, Atsuhiro
Format: Artikel
Sprache:eng
Schlagworte:
4-connected
Even triangulations
Generating theorem
Graphs
Mathematical analysis
Octahedrons
Sequences
Sphere
Transformations (mathematics)
Triangulation
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Zusammenfassung:In this paper, we prove that every 4-connected even triangulation on the sphere can be obtained from the octahedron by a sequence of two kinds of transformations called a 4-splitting and a twin-splitting, only through 4-connected even triangulations. As a corollary, taking a dual, we can also generate all cyclically 4-edge-connected cubic bipartite graphs on the sphere.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2014.08.017