please - help - what does mean singly-connected set? this is set without holes and which has one bounded contour? the sample http://doc.cgal.org/latest/Straight_skeleton_2/index.html#Chapter_2D_Straight_Skeleton_and_Polygon_Offsetting means that this is set of another structure or this docs has mistake?
At least in the Straight skeleton package it means that if you strip off the boundary of the polygon, any two points of the open polygon can be connected with a curve inside the open polygon.