Undergraduate projects on graph theory

I began my career as a research mathematician as an undergraduate at Dartmouth College where I worked with Ken Bogart. With him, I worked on a project on sphere-of-influence graphs. These are intersection graphs of a set of spheres in the plane. I continued worked on a second graph theory project at the Duluth REU in Duluth, MN, under the supervision of Joe Gallian. Here are the papers that I wrote during this time.

On tolerance sphere-of-influence graphs
(with Kenneth Bogart) Bull. Inst. Combin. Appl. 24 (1998) 33--46.
Preprint available in gzipped postscript.
This is a study of sphere-of-influence graphs. We look not at the intersections of a set of circles in the plane, but instead add and edge when the intersection is ``big enough.''
On majority domination graphs
Discrete Math. 239 (2001) 1--12.
Preprint available in gzipped postscript.
This is a problem about the domination statistic for a graph
Tolerance sphere-of-influence graphs
Senior Honors Thesis, Dartmouth College, 1997.
Available in gzipped postscript.
This is a complete exposition of sphere-of-influence graphs, along with the results of the first paper.