Deformable Polygon Representation and Near-Mincuts [chapter]

András A. Benczúr, Michel X. Goemans
2008 Bolyai Society Mathematical Studies  
We derive a necessary and sufficient condition for a symmetric family of sets to have a geometric representation involving a convex polygon and some of its diagonals. We show that cuts of value less than 6/5 times the edge-connectivity of a graph admit such a representation, thereby extending the cactus representation of all mincuts. In descriptions of the cactus representation, the cycles of length 2 are sometimes replaced by a single edge (bridge) of weight 2. 2 To easily distinguish them, we
more » ... istinguish them, we use vertices for the graph G and nodes for the cactus H.
doi:10.1007/978-3-540-85221-6_3 fatcat:rnk2dcxsxbh3dg542jq57ob6w4