Dr. Glenn Hurlbert
Virginia Commonwealth University
Talk is at 10:00 AM Central Time (calculating your local time…)
Abstract
Graph pebbling began as a method to solve zero-sum problems in combinatorial number theory and group theory. Like many "games" that move tokens along the edges of a graph according to various rules (e.g., cops & robbers, zero forcing, power domination, graph burning, etc.), it has grown into a network optimization model in its own right. The fundamental invariant in the subject is called the pebbling number of a graph, which is the minimum number t such that any supply of t pebbles can satisfy any specified demand in the graph.
Graham’s Conjecture has driven a great deal of work since its inception in 1989. It posits that the pebbling number of a Cartesian product of two graphs is bounded from above by the product of the pebbling numbers of the individual graphs. Here we will describe some of the methods used on this problem and illustrate several key results, focusing in particular on recent theorems of Herscovici that one might hope to generalize.