Rectilinear Graphs and Angular Resolution

Abstract

In this note we show that a planar graph with angular resolution at least π/2 can be drawn with all angles an integer multiple of π/2, that is, in a rectilinear manner. Moreover, we show that for d ≠ 4, d › 2, having an angular resolution of 2π/d does not imply that the graph can be drawn with all angles an integer multiple of 2π/d. We argue that the exceptional situation for d = 4 is due to the absence of triangles in the rectangular grid.