Grid Embedding of Internally Triangulated Plane Graphs without Non-empty Triangles

A straight line grid embedding of a plane graph G is a drawing of G such that the vertices are drawn at grid points and the edges are drawn as non-intersecting straight line segments. In this paper, we show that, if an internally triangulated plane graph G has no non-empty triangles (a non-empty triangle is a triangle of G containing some vertices in its interior), then G can be embedded on a grid of size W H such that W + H n, W (n + 3)=2 and H 2(n ? 1)=3, where n is the number of vertices of G. Such an embedding can be computed in linear time.