On the number of internal and external visibility edges of polygons

In this paper we prove that for any simple polygon P with n vertices, the sum of the number of strictly internal edges and the number of strictly external visibility edges of P is at least 3n−1 2 − 4. The internal visibility graph of a simple polygon P is the graph with vertex set equal to the vertex set of P, in which two vertices are adjacent if the line segment connecting them does not intersect the exterior of P. The external visibility graph of P is defined in a similar way, except that the line segments that generate its edges are not allowed to intersect the interior of P. A visibility edge is called strictly internal (resp. strictly external) if it is not an edge of P. In this paper we prove the following conjecture of Bagga [1]: For any simple polygon P with n vertices, the number of strictly internal visibility edges plus the number of strictly external visibility edges is at least 3n−1 2 − 4. In Figure 1 we present a family of polygons that achieve this bound. They...

• Type: Conference
• Year: 1997
• Where: CCCG
• Authors: Jorge Urrutia
• Keywords: CCCG 1997, CCCG 2007, External Visibility Edges, Simple Polygon, Visibility Edges