Geodesic
Rook-drawings of Plane Graphs
Journal of Graph Algorithms and Applications, Special Issue on Selected papers from the Twenty-third International Symposium on Graph Drawing and Network Visualization, GD 2015 , Tome 21 (2017) no. 1, pp. 103-120.

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We introduce a new type of graph drawing called "rook-drawing". A rook-drawing of a graph $G$ is obtained by placing the $n$ nodes of $G$ on the intersections of a regular grid, such that each row and column of the grid supports exactly one node. This paper focuses on rook-drawings of planar graphs. We first give a linear algorithm to compute a planar straight-line rook-drawing for outerplanar graphs. We then characterize the maximal planar graphs admitting a planar straight-line rook-drawing, which are unique for a given order. Finally, we give a linear time algorithm to compute a polyline planar rook-drawing for plane graphs with at most $n-3$ bent edges.
DOI : 10.7155/jgaa.00402
Keywords: graph drawing, straight-line drawing, planar graph, polyline drawing 
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David Auber; Nicolas Bonichon; Paul Dorbec; Claire Pennarun. Rook-drawings of Plane Graphs. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected papers from the Twenty-third International Symposium on Graph Drawing and Network Visualization, GD 2015
					, Tome 21 (2017) no. 1, pp. 103-120. doi : 10.7155/jgaa.00402. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00402/

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