Trémaux trees and planarity

Hubert de Fraysseix (1) , Patrice Ossona de Mendez (1) , Pierre Rosenstiehl (1)

1 CAMS - Centre d'Analyse et de Mathématique sociales

We present a simplified version of the DFS-based Left-Right planarity testing and embedding algorithm implemented in Pigale which has been considered as the fastest implemented one [J.M. Boyer, P.F. Cortese, M. Patrignani, and G. Di Battista. Stop minding your P's and Q's: implementing fast and simple DFS-based planarity and embedding algorithm. In Graph Drawing, volume 2912 of Lecture Notes in Computer Science, pages 25-36. Springer, 2004.]. We give here a simple full justification of the algorithm, based on a preliminary extended study of topological properties of DFS trees.

Mots clés: Depth-First Search; Planarity algorithm

Domaines: Combinatoire [math.CO]

Hubert de Fraysseix, Patrice Ossona de Mendez, Pierre Rosenstiehl. Trémaux trees and planarity. International Journal of Foundations of Computer Science, 2006, 17 (5), pp.1017-1029. ⟨10.1142/S0129054106004248⟩. ⟨hal-00097836⟩