Classes of arrangement graphs in three dimensions

A 3D arrangement graph G is the abstract graph induced by an arrangement of planes in general position where the intersection of any two planes forms a line of intersection and an intersection of three planes creates a point. The properties of three classes of arrangement graphs — four, five and six planes — are investigated. For graphs induced from six planes, specialized methods were developed to ensure all possible graphs were discovered. The main results are: the number of 3D arrangement graphs induced by four, five and six planes are one, one and 43 respectively; the three classes are Hamiltonian; and the 3D arrangement graphs created from four and five planes are planar but none of the graphs created from six planes are planar.

Authors

• Nickle, Elspeth J.
• University of Lethbridge. Faculty of Arts and Science

• Graph theory
• Computer graphics
• Geometrical constructions
• Graphic methods
• Dissertations, Academic

Identifier

hdl:10133/632

OAI identifier oai:identifier

oai:opus.uleth.ca:10133/632