We show that every finite connected graph G with maximum degree three and with at least one vertex of degree smaller than three has a straight-line drawing in the plane satisfying the following conditions. No three vertices are collinear, and a pair of vertices form an edge in G if and only if the segment connecting them is parallel to one of the sides of a previously fixed regular pentagon. It is also proved that every finite graph with maximum degree three permits a straight-line drawing with the above properties using only at most seven different edge slopes. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Keszegh, B., Pach, J., Pálvölgyi, D., & Tóth, G. (2009). Cubic graphs have bounded slope parameter. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5417 LNCS, pp. 50–60). Springer Verlag. https://doi.org/10.1007/978-3-642-00219-9_6
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