A Left-First Search Algorithm for Planar Graphs.

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

1 CAMS - Centre d'Analyse et de Mathématique sociales

We give an O(|V(G)|)-time algorithm to assign vertical and horizontal segments to the vertices of any bipartite plane graph G so that (i) no two segments have an interior point in common, (ii) two segments touch each other if and only if the corresponding vertices are adjacent. As a corollary, we obtain a strengthening of the following theorem of Ringel and Petrovic. The edges of any maximal bipartite plane graph G with outer face bwb'w' can be colored by two colors such that the color classes form spanning trees of G-b and G-b', respectively. Furthermore, such a coloring can be found in linear time. Our method is based on a new linear-time algorithm for constructing bipolar orientations of 2-connected plane graphs.

Domaines: Combinatoire [math.CO]

Hubert de Fraysseix, Patrice Ossona de Mendez, Janos Pach. A Left-First Search Algorithm for Planar Graphs.. Discrete and Computational Geometry, 1995, 13, pp.459-468. ⟨hal-00005623⟩