Drawability of Complete Graphs Using a Minimal Slope Set
G. A. Wade, Jun Chu · The Computer Journal · 1994
In this paper we will study the problem of drawing graphs with a minimum number of slopes. We will show that the minimum number of slopes needed to draw a complete graph of n vertices is n. We will also prove that for a complete graph of n vertices to be drawn using only n slopes its vertices must form a convex polygon. Finally, we will present an algorithm which checks whether a complete graph of n vertices can be drawn using only slopes from a given set of n slopes.