Carl R. Yerger

Harvey Mudd College Mathematics 2005

Thesis Proposal: Proposal
Thesis: Extensions of Graph Pebbling
Thesis Poster: Poster
Thesis Advisor: Prof. Francis Edward Su
Second Reader: Prof. Anant Godbole

Thesis Abstract

My thesis will consist of extensions to results that I proved at the 2004 East Tennessee State REU. Most of these results have to do with graph pebbling and various probabilistic extensions. Specifically, in Chapter 2 we compute the cover pebbling number for complete multipartite graphs and prove upper bounds for cover pebbling numbers for graphs of a specified diameter and order. We also prove that the cover pebbling decision problem is NP complete. In Chapters 3 and 4 we examine domination cover pebbling. In Chapter 5, we obtain structural and probabilistic results for deep graphs, and in Chapter 6 we compute cover pebbling probability thresholds for the complete graph.

Future Plans

This summer I plan on teaching at the Pennsylvania Governor's School for the Sciences at Carnegie Mellon University. In the fall, I will be taking Part III of the Mathematical Tripos at Cambridge University on a Winston Churchill Foundation Scholarship. In Fall 2006, I plan to study at the Georgia Institute of Technology in the Algorithms, Combinatorics and Optimization doctoral program, and I will be funded by a National Science Foundation fellowship.