Geodesic
Characterizing Families of Cuts that can be Represented by Axis-Parallel Rectangles
Journal of Graph Algorithms and Applications, Special Issue on Selected Papers from the Eleventh International Symposium on Graph Drawing, GD 2003 , Tome 9 (2005) no. 1, pp. 99-115.

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A drawing of a family of cuts of a graph is an augmented drawing of the graph such that every cut in the family is represented by a simple closed curve and vice versa. We show that the families of cuts that admit a drawing in which every cut is represented by an axis-parallel rectangle are exactly those that have a cactus model that can be rooted such that edges of the graph that cross a cycle of the cactus point to the root. This includes the family of all minimum cuts of a graph. The proof also yields an efficient algorithm to construct a drawing with axis-parallel rectangles if it exists. 
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     title = {Characterizing {Families} of {Cuts} that can be {Represented} by {Axis-Parallel} {Rectangles}},
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Ulrik Brandes; Sabine Cornelsen; Dorothea Wagner. Characterizing Families of Cuts that can be Represented by Axis-Parallel Rectangles. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected Papers from the Eleventh International Symposium on Graph Drawing, GD 2003
					, Tome 9 (2005) no. 1, pp. 99-115. doi : 10.7155/jgaa.00101. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00101/

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