Grünbaum colorings of toroidal triangulations

2010 ◽  
Vol 63 (1) ◽  
pp. 68-81 ◽  
Author(s):  
Michael O. Albertson ◽  
Hannah Alpert ◽  
sarah-marie belcastro ◽  
Ruth Haas
Keyword(s):  
Toroidal Triangulations

scholarly journals Encoding Toroidal Triangulations

2016 ◽  
Vol 57 (3) ◽  
pp. 507-544 ◽  
Author(s):  
Vincent Despré ◽  
Daniel Gonçalves ◽  
Benjamin Lévêque
Keyword(s):  
Toroidal Triangulations

scholarly journals A Bijection for Essentially 4-Connected Toroidal Triangulations

10.37236/7897 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Nicolas Bonichon ◽  
Benjamin Lévêque
Keyword(s):  
Distributive Lattice ◽  
Minimal Element ◽  
Distributive Lattices ◽  
Outer Face ◽  
Random Generation ◽  
Combinatorial Structures ◽  
Toroidal Triangulations

Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications (drawing algorithm, random generation, enumeration, ...). In this paper we introduce and study a generalization of these objects for the toroidal case. Contrary to what happens in the plane, the set of toroidal transversal structures of a given toroidal triangulation is partitioned into several distributive lattices. We exhibit a subset of toroidal transversal structures, called balanced, and show that it forms a single distributive lattice. Then, using the minimal element of the lattice, we are able to enumerate bijectively essentially 4-connected toroidal triangulations.

Hamiltonicity of 5-Connected Toroidal Triangulations

1995 ◽  
Vol 20 (3) ◽  
pp. 267-286 ◽  
Author(s):  
Richard Brunet ◽  
R. Bruce Richter
Keyword(s):  
Toroidal Triangulations
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