Draw a picture of a simple polygon and a set of guards, such that the guards can see every point on every edge of the polygon, but the guards cannot see every point in the interior of the polygon.
I encountered this while randomly searching for polygon triangulation problems. I feel that no such polygon + guard combination exists. but I do not know how to go about proving or disproving that. Some help would be appreciated.
Source: Page 17, Problem 1(a) on this document
This should do it. Yellow stars are the guards. They cannot see the red object.