Cubic graphs have bounded slope parameter - Keszegh, Balázs; Pach, János; Pálvölgyi, Dömötör; Tóth, Géza (Journal of Graph Algorithms and Applications, 2010)
We show that every finite connected graph G with maximum degreethree and with at least one vertex of degree smaller thanthree has a straight-line drawing in the plane satisfyingthe following conditions. No three vertices are collinear, and apair of vertices form an edge in G if and only if the segmentconnecting them is parallel to one of the sides of a previouslyfixed regular pentagon. It is also proved that every finite graphwith maximum degree three permits a straight-line drawingwith the above properties using at most seven differentedge slopes. <!---->