Characterizing Families of Cuts That Can Be Represented by Axis-Parallel Rectangles

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. Article Type Communicated by Submitted Revised regular paper G. Liotta January 2004 July 2005 Research partially supported by the DFG under grant BR 2158/1-1,2 and WA 654/131,2 and by the Human Potential Program of the EU under contract no HPRN-CT1999-00104 (AMORE Project). 

• Type: Conference
• Year: 2003
• Where: GD
• Authors: Ulrik Brandes, Sabine Cornelsen, Dorothea Wagner
• Keywords: Augmented Drawing, Axis-parallel Rectangles, GD 2003, Simple Closed Curve