Drawing cubic graphs with the four basic slopes
  We show that every cubic graph can be drawn in the plane with straight-line edges using only the four basic slopes $\{0,\pi/4,\pi/2,3\pi/4\}$. We also prove that four slopes have this property if and only if we can draw $K_4$ with them. 
Padmini Mukkamala and D\"om\"ot\"or P\'alv\"olgyi
math.CO cs.DM