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:

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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.

Item Type:Conference Paper
Additional Information:10.1007/978-3-642-00219-9_6
Classifications:P Styles > P.720 Straight-line
Z Theory > Z.250 Geometry
ID Code:894

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