Title: Zero Forcing and Vertex Induced Subgraphs

Abstract: Zero forcing is a coloring propagation process on finite graphs, which can be considered a one player game. In this talk we will consider recent findings in zero forcing concerning monotonicity. While the zero forcing number of a graph is not monotone with respect to its subgraphs, we can still use certain graph substructures created during the propagation process to preserve a sense of monotonicty. We will consider this problem from two directions, first we will look at the vertex induced subgraphs associated with cut-sets of a graph, and second we will construct supergraphs from sequences of graphs in a way prescribed by another graph theoretical game with roots in the work of Erdos.