How to draw the minimum cuts of a planar graph

Authors:
Ulrik Brandes;Sabine Cornelsen;Christian Fieß;Dorothea Wagner
Affiliations:
Fachbereich Informatik & Informationswissenschaft, Universitäät Konstanz, Germany;Fachbereich Informatik & Informationswissenschaft, Universitäät Konstanz, Germany;SMA und Partner AG, Zürich, Switzerland;Fakultät für Informatik, Universität Karlsruhe, Germany
Venue:
Computational Geometry: Theory and Applications
Year:
2004

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Abstract

We show how to utilize the cactus representation of all minimum cuts of a graph to visualize the minimum cuts of a planar graph in a planar drawing. In a first approach the cactus is transformed into a hierarchical clustering of the graph that contains complete information on all the minimum cuts. This approach is then extended to drawings in which the two vertex subsets of every minimum cut are separated by a simple closed curve. While both approaches work with any embedding-preserving drawing algorithm, we specifically discuss bend-minimum orthogonal drawings.