Department Colloquium

Thu., Oct. 5, 2023 2:30 p.m.

Location: RIC 209

Speaker: Glenn Hurlbert, Virginia Commonwealth University

Title: Pebbling Problems and Paradigms (83 kB)

Abstract:

There are many areas in graph theory and optimization that could all go under the umbrella of Moving Stff Around in Graphs - graph pebbling is one of them; domination, network optimization, cops and robbers, max ow, zero-forcing, and graph burning are among other examples. In graph pebbling we encounter a configuration of pebbles on the vertices of a graph and are allowed to make moves by removing two pebbles from some vertex and placing one pebble on one of its neighbors. For a specific target vertex we ask if it is possible to place a pebble on it after a sequence of pebbling moves. From here, a range of invariants (pebbling numbers of various types) can be explored, each measuring what size of initial configuration is required to reach a target. We will introduce the audience to this intriguing topic, share a few nice results, and leave you with a few problems to ponder.