Classes of arrangement graphs in three dimensions
Elspeth Nickle · Open ULeth Scholarship (OPUS) (University of Lethbridge) · 2005
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.iii my work In addition, I wish to extend a special thanks to the University of Lethbridge in general, and the Department of Mathematics and Computer Science in particular, for a very positive and supportive environment in which to study.I also enjoyed my fellow students in the Computational Geometry Laboratory who never ceased to provide fun, interest and help when needed.Finally, but far from least, I am deeply indebted to my husband, Ron Teather, for his inexhaustible support, his unwavering love -and for putting up with all my erratic hours.