A bijection for essentially 4-connected toroidal triangulations
| Autor: | Bonichon, Nicolas, Lévêque, Benjamin |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 67 pages. arXiv admin note: text overlap with arXiv:1702.07589 |
| Databáze: | arXiv |
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