How to draw the minimum cuts of a planar graph

How to draw the minimum cuts of a planar graph

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 ar...

How to Draw the Minimum Cuts of a Planar Graph (Extended 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 ar...

How to Draw the Minimum

On How to Draw a Graph

We give an overview of Tutte’s paper, “How to draw a graph”, that contains: (i) a proof that every simple 3-connected planar graph admits a straight-line embedding in the plane such that each face boundary is a convex polygon, (ii) an elegant algorithm for finding such an embedding, (iii) an algorithm for testing planarity, and (iv) a proof of Kuratowski’s theorem.

On the Number of Minimum Cuts in a Graph

We relate the number of minimum cuts in a weighted undirected graph with various structural parameters of the graph. In particular, we provide upper bounds for the number of minimum cuts in terms of the radius, diameter, minimum degree, maximum degree, chordality, girth, and some other parameters of the graph.