Planarity and Trémaux trees

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

1 CAMS - Centre d'Analyse et de Mathématique sociales

We present a characterization of planarity based on Trémaux trees (i.e. DFS trees), from which we deduce a simple and efficient planarity test algorithm. We finally recall a theorem on ''cotree critical non-planar graphs" which very much simplify the search of a Kuratowski subdivision in a non-planar graph.

Domaines: Combinatoire [math.CO]

Hubert de Fraysseix, Patrice Ossona de Mendez. Planarity and Trémaux trees. European Journal of Combinatorics, 2012, 33 (3), pp.279-293. ⟨10.1016/j.ejc.2011.09.012⟩. ⟨hal-00656808⟩