Cubic Graphs Have Bounded Slope Parameter
Keszegh, Balázs and Pach, János and Pálvölgyi, Dömötör and Tóth, Géza (2009) Cubic Graphs Have Bounded Slope Parameter. In: Graph Drawing 16th International Symposium, GD 2008, September 21- 24, 2008, Heraklion, Crete, Greece , pp. 50-60 (Official URL: http://dx.doi.org/10.1007/978-3-642-00219-9_6).
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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.
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