Research

What is throttling?

Most of my research is on the concept of throttling. Consider a process that requires initial resources and also takes time to complete. A perfect example is the process of spreading information across a network. The idea of throttling is to find the right balance between the amount of initial resources and the completion time so that the process is as effective as possible. By starting with the right initial resources, we can dramatically speed up (or throttle) the process. A graph is a collection of vertices or nodes together with a collection of edges which can be represented as line segments that connect one vertex to another. There are many processes in graph theory that can be throttled. I study throttling for a process called "zero forcing" as well as a game called "cops and robbers". For details on throttling for zero forcing, see the video below.

This is me speaking at the Mostly Manitoba, Michigan, and Minnesota Combinatorics Workshop.

Publications

Accepted:

Throttling positive semidefinite zero forcing propagation time on graphs (with Hogben et al.). Discrete Applied Mathematics, in press, https://doi.org/10.1016/j.dam.2018.06.017.
Throttling for the game of Cops and Robbers on graphs (with Breen et al.). Discrete Mathematics, 341 (2018), 2418-2430.
Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs (with Berliner et al.). Involve, 8 (2015), 147-167.

Under Review:

Power domination throttling (with Brimkov et al.). https://arxiv.org/abs/1810.01009
Throttling for zero forcing and variants. https://arxiv.org/abs/1807.07030
Ordered multiplicity inverse eigenvalue problem for graphs on six vertices (with Ahn et al.). https://arxiv.org/abs/1708.02438

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