Skip to Main content Skip to Navigation
Journal articles

A Left-First Search Algorithm for Planar Graphs.

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00005623
Contributor : Patrice Ossona de Mendez Connect in order to contact the contributor
Submitted on : Friday, August 19, 2005 - 12:11:48 PM
Last modification on : Friday, July 17, 2020 - 9:17:47 AM
Long-term archiving on: : Thursday, April 1, 2010 - 9:46:54 PM

Files

Identifiers

  • HAL Id : hal-00005623, version 1

Collections

Citation

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

Share

Metrics

Record views

361

Files downloads

511