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

  • Ulrik Brandes
  • Sabine Cornelsen
  • Dorothea Wagner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Sabine Cornelsen
    • 2
  • Dorothea Wagner
    • 3
  1. 1.Fakultät für Mathematik & InformatikUniversität Passau 
  2. 2.Dipartimento di Ingegneria ElettricaUniversità dell’Aquila 
  3. 3.Fakultät für InformatikUniversität Karlsruhe 

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