Geodesic
Non-aligned Drawings of Planar Graphs
Journal of Graph Algorithms and Applications, Special issue on Selected papers from the Twenty-fourth International Symposium on Graph Drawing and Network Visualization, GD 2016 , Tome 21 (2017) no. 5, pp. 915-937.

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A non-aligned drawing of a graph is a drawing where no two vertices are in the same row or column. Auber et al. showed that not all planar graphs have a non-aligned planar straight-line drawing in the $n\times n$-grid. They also showed that such a drawing exists if up to $n-3$ edges may have a bend. In this paper, we give algorithms for non-aligned planar drawings that improve on the results by Auber et al. In particular, we give such drawings on an $n\times n$-grid with at most $\frac{2n-5}{3}$ bends, and we study what grid-size can be achieved if we insist on having straight-line drawings.
DOI : 10.7155/jgaa.00444
Keywords: planar graph, straight-line drawing, grid drawing, polyline drawing 
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Therese Biedl; Claire Pennarun. Non-aligned Drawings of Planar Graphs. Journal of Graph Algorithms and Applications, 
							Special issue on Selected papers from the Twenty-fourth International Symposium on Graph Drawing and Network Visualization, GD 2016
					, Tome 21 (2017) no. 5, pp. 915-937. doi : 10.7155/jgaa.00444. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00444/

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