A Left-First Search Algorithm for Planar Graphs
De Fraysseix, Hubert and Ossona de Mendez, Patrice and Pach, János (1995) A Left-First Search Algorithm for Planar Graphs. [Journal (Paginated)]
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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.
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