Geodesic
Not all planar graphs are in PURE-4-DIR
Journal of Graph Algorithms and Applications, Tome 24 (2020) no. 3, pp. 293-301.

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We prove that some planar graphs are not intersection graphs of segments if only four slopes are allowed for the segments, and if parallel segments do not intersect. This refutes a conjecture of D. West [D. West, SIAM J. Discrete Math. Newsletter, 1991].
DOI : 10.7155/jgaa.00533
Keywords: intersection graphs, planar graphs, segments 
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     title = {Not all planar graphs are in {PURE-4-DIR}},
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Daniel Gonçalves. Not all planar graphs are in PURE-4-DIR. Journal of Graph Algorithms and Applications, Tome 24 (2020) no. 3, pp. 293-301. doi : 10.7155/jgaa.00533. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00533/

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