How to draw the minimum cuts of a planar graph

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. We present an algorithm for c-planar orthogonal drawings of hierarchically clustered planar graphs with rectangularly shaped cluster boundaries and the minimum number of bends. This approach is then extended to drawings in which the two vertex subsets of every minimum cut are separated by a simple closed curve.