This talk will begin with a brief discussion of motivations for conducting research in mathematics and why the presenter believes that graph pebbling is an appealing research area. It will continue with an introduction to graph pebbling. A survey of several streams of pebbling research, including cover pebbling, optimal pebbling and Class 0 graphs will be discussed. A number of accessible results (many involving undergraduates) and some open problems will also be presented.

Graph pebbling is a combinatorial game played on an undirected graph with an initial configuration of pebbles. A pebbling move consists of removing two pebbles from one vertex and placing one pebbling on an adjacent vertex. The pebbling number of a graph is the smallest number of pebbles necessary such that, given any initial configuration of pebbles, at least one pebble can be moved to a specified target vertex.

Bio

Carl Yerger is a professor and former chair of the Department of Mathematics and Computer Science at Davidson College, where he has been a faculty member since 2010. After graduating from Harvey Mudd College in 2005, Carl took Part III of the Mathematical Tripos as a Churchill Scholar at Cambridge University in 2006 and then earned a Ph.D. in Algorithms, Combinatorics, and Optimization from Georgia Tech in 2010. His mathematical interests are structural graph theory, combinatorics, and Ramsey theory. In addition, he has served as Co-Editor-in-Chief of the MAA’s AMC 10/12 exam since 2017 and helps organize the Charlotte Mathematics Club. Outside of mathematics, Carl is an avid tennis player and currently serves as secretary of the United States Korfball Federation.