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, and (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 Petrovič. 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. © 1995 Springer-Verlag New York Inc.