Research
What is throttling?
My main 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.
Current Projects
Chapter on games on graphs for Foundations of Undergraduate Research in Mathematics series (with Harris, Hollander, and Insko)
Throttling for the hopping rule (with Petrucci)
Throttling for positive semidefinite zero forcing on directed graphs (with Kitchen)
Bounds for b-invisible rectangles (with Estupiñan et al.)
Publications
Accepted:
Ordered multiplicity inverse eigenvalue problem for graphs on six vertices (with Ahn et al.). To appear in Electron. J. Linear Algebra, preprint available at https://arxiv.org/abs/1708.02438.
Parking functions: Choose your own adventure (with Christensen et al.). To appear in College Math J., preprint available at https://arxiv.org/abs/2001.04817.
Antimagic orientations of graphs with large maximum degree (with Yang et al.). Discrete Math., 343 (2020), 112--123.
Sequences of consecutive factoradic happy and semihappy numbers (with Goedhart and Harris). Rocky Mountain J. Math., 50 (2020), 1241--1252.
Power Domination Throttling (with Brimkov et al.). Theoret. Comput. Sci., 795 (2019), 142--153.
Throttling for Zero Forcing and Variants. Australas. J. Combin., 75 (2019), 96-112.
Throttling positive semidefinite zero forcing propagation time on graphs (with Hogben et al.). Discrete Appl. Math., 254 (2019), 33-46.
Throttling for the game of Cops and Robbers on graphs (with Breen et al.). Discrete Math., 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:
Throttling for standard zero forcing on directed graphs (with Cairncross et al.). Under review, preprint available at https://arxiv.org/abs/2008.08646.
The damage throttling number of a graph (with Eagleton et al.). Under review, preprint available at https://arxiv.org/abs/2006.10894.
Various characterizations of throttling numbers (with Kritschgau). https://arxiv.org/abs/1909.07952
Optimizing the trade-off between number of cops and capture time in Cops and Robbers (with Bonato et al.). Under review, preprint available at https://arxiv.org/abs/1903.10087.