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Morrison, Sara Alaina

Mathematics

2004

M.S.

The goal of this research is to determine the specific conditions under which we can find a simple planar graph G that admits a packing of multiple copies of a tree. This is equivalent to finding a planar graph G which has an edge partition such that each part is isomorphic to the given tree. We begin by looking at paths, stars, and the Ok,k graph, defined as a tree with 2 vertices of degree k and all other vertices of degree 1. We restrict our studies to the tight packing, where the planar graph G is a triangulation. Tight packings occur with six copies of the tree on 2n vertices and three copies of the tree on n + 1 vertices. We also discuss extensions of our results as directions for future studies.