Journal of Graph Algorithms and Applications
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Not all planar graphs are in PURE-4-DIR
Vol. 24, no. 3, pp. 293-301, 2020. Concise paper.
Abstract 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].
Submitted: October 2019.
Reviewed: February 2020.
Revised: February 2020.
Accepted: May 2020.
Final: May 2020.
Published: June 2020.
Communicated by Martin Nöllenburg