@inbook{de41f4f2adcb4b80a13910c6fc209c6b,
title = "Optimal coding and sampling of triangulations",
abstract = "We present a bijection between the set of plane triangulations (aka. maximal planar graphs) and a simply defined subset of plane trees with two leaves per inner node. The construction takes advantage of the minimal realizer (or Schnyder tree decomposition) of a plane triangulation. This yields a simple interpretation of the formula for the number of plane triangulations with n vertices. Moreover the construction is simple enough to induce a linear random sampling algorithm, and an explicit information theory optimal encoding.",
author = "Dominique Poulalhon and Gilles Schaeffer",
year = "2003",
month = jan,
day = "1",
doi = "10.1007/3-540-45061-0\_83",
language = "English",
isbn = "3540404937",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "1080--1094",
editor = "Baeten, \{Jos C. M.\} and Lenstra, \{Jan Karel\} and Joachim Parrow and Woeginger, \{Gerhard J.\}",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
}