On the Number of Acute Triangles in a Straight-Line Embedding of a Maximal Planar Graph

In this paper we show that any maximal planar graph withmtriangles except the unbounded face can be transformed into a straight-line embedding in which at least ⌉m/3⌉ triangles are acute triangles. Moreover, we show that any maximal outer-planar graph can be transformed into a straight-line embedding in which all faces are acute triangles except the unbounded face.