Not all planar graphs are in PURE-4-DIR - Gonçalves, Daniel (Journal of Graph Algorithms and Applications, 2020)
We prove that some planar graphs are not intersection graphs ofsegments if only four slopes are allowed for the segments, and ifparallel segments do not intersect. This refutes a conjecture ofD. West [D. West, SIAM J. Discrete Math. Newsletter, 1991].