Geodesic
Drawing Graphs on Two and Three Lines
Journal of Graph Algorithms and Applications, Special Issue on Selected Papers from the Tenth International Symposium on Graph Drawing, GD 2002 , Tome 8 (2004) no. 2, pp. 161-177.

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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. We utilize this result to obtain planar drawings on three lines for a generalization of bipartite graphs, also in linear time. 
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     title = {Drawing {Graphs} on {Two} and {Three} {Lines}},
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Sabine Cornelsen; Thomas Schank; Dorothea Wagner. Drawing Graphs on Two and Three Lines. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected Papers from the Tenth International Symposium on Graph Drawing, GD 2002
					, Tome 8 (2004) no. 2, pp. 161-177. doi : 10.7155/jgaa.00087. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00087/

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