On the number of acute triangles in a straight-line embedding of a maximal planar graph (Q1306427)

We show that any maximal planar graph with \(m\) triangles except the unbounded face can be transformed into a straight-line embedding in which at least \(\lceil m/3\rceil\) 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. \(\copyright\) Academic Press.