A bijection between realizers of maximal plane graphs and pairs of non-crossing Dyck paths

@article{Bonichon2005ABB,
  title={A bijection between realizers of maximal plane graphs and pairs of non-crossing Dyck paths},
  author={Nicolas Bonichon},
  journal={Discrete Mathematics},
  year={2005},
  volume={298},
  pages={104-114}
}
Schnyder trees, or realizers, ofmaximal plane graphs, arewidely used in the graph drawing domain. In this paper, a bijection between realizers and pairs of non-crossing Dyck paths is proposed. The transformation of a realizer into a pair of non-crossing Dyck paths and the opposite operation can be done in linear time. Applying this bijection, we enumerate the number of realizers of size n and we can efficiently generate all of them. Résumé Les arbres de Schnyder, ou réaliseurs, d’un… CONTINUE READING