Characterizing Families of Cuts That Can Be Represented by Axis-Parallel Rectangles
Brandes, Ulrik and Cornelsen, Sabine and Wagner, Dorothea (2004) Characterizing Families of Cuts That Can Be Represented by Axis-Parallel Rectangles. In: Graph Drawing 11th International Symposium, GD 2003, September 21-24, 2003, Perugia, Italy , pp. 357-368 (Official URL: http://dx.doi.org/10.1007/978-3-540-24595-7_33).
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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 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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