Disjoint Segments Have Convex Partitions with 2-Edge Connected Dual Graphs

The empty space around n disjoint line segments in the plane can be partitioned into n + 1 convex faces by extending the segments in some order. The dual graph of such a partition is the plane graph whose vertices correspond to the n+1 convex faces, and every segment endpoint corresponds to an edge between the two incident faces on opposite sides of the segment. We construct, for every set of n disjoint line segments in the plane, a convex partition whose dual graph is 2-edge connected.

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Nadia Benbernou, Erik D. Demaine, Martin L. Demaine, Michael Hoffmann, Mashhood Ishaque, Diane L. Souvaine, Csaba D. Tóth
• Keywords: CCCG 2007, Computational Geometry, Convex Faces, Disjoint Line Segments, Dual Graph