Cubic Graphs Have Bounded Slope ParameterKeszegh, 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 , pp. 5060(Official URL: http://dx.doi.org/10.1007/9783642002199_6). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783642002199_6
AbstractWe show that every ﬁnite connected graph G with maximum degree three and with at least one vertex of degree smaller than three has a straightline 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 straightline drawing with the above properties using only at most seven different edge slopes.
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