Lecture Notes in Computer Science Volume 2528, 2002, pp 31-41

Drawing Graphs on Two and Three Lines

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We give a linear-time algorithm to decide whether a graph has a planar LL-drawing, i.e. a planar drawing on two parallel lines. This has previously been known only for trees. We utilize this result to obtain planar drawings on three lines for a generalization of bipartite graphs, also in linear time.