Convex drawings of graphs with non-convex boundary constraints

: In this paper, we study a new problem of convex drawing of planar graphs with non-convex boundary constraints. It is proved that every triconnected plane graph whose boundary is fixed with a star-shaped polygon admits a drawing in which every inner facial cycle is drawn as a convex polygon. We also prove that every four-connected plane graph whose boundary is fixed with a crown-shaped polygon admits such a drawing, called an inner-convex drawing. We present an algorithm to construct an inner-convex drawing in linear time.

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Seok-Hee Hong, Hiroshi Nagamochi
• Keywords: DAM 2008, Inner-convex Drawing, Non-convex Boundary Constraints, Plane Graph