We show that every cubic graph can be drawn in the plane with straight-line edges using only the four basic slopes {0,π/4,π/2,3π/4}. We also prove that four slopes have this property if and only if we can draw K4 with them.
@article{arxiv.1106.1973,
title = {Drawing cubic graphs with the four basic slopes},
author = {Padmini Mukkamala and Dömötör Pálvölgyi},
journal= {arXiv preprint arXiv:1106.1973},
year = {2011}
}