Puck Rombach

Assistant Professor at the Department of Mathematics and Statistics, University of Vermont.

Graduate Program Coordinator for the MS and PhD in Mathematical Sciences Programs (mathematics track).

My main research interests are in structural and extremal graph theory, probability, and algorithms and complexity. I also enjoy learning about applications of discrete mathematics through interdisciplinary collaborations.

I teach a variety of classes, including combinatorics, graph theory, analysis and algebra.

Graduate Research Students

Calum Buchanan, Jo Martin (MS thesis), Hunter Rehm

Publications

Extremal Graph Theory
Rainbow Saturation, Neal Bushaw, Daniel Johnston, Puck Rombach; arXiv:2003.13200, 2020.
Lower bounds for rainbow Turán numbers of paths and other trees, Daniel Johnston, Puck Rombach; Australasian Journal of Combinatorics, 78(1), 2020.

Symmetry Breaking
Determining Number and Cost of Generalized Mycielskian Graphs, Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach; arXiv:2007.15284, 2020.
Distinguishing Generalized Mycielskian Graphs, Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach; arXiv:2006.03739, 2020.

Guessing Numbers and Entropy
Guessing Numbers and Extremal Graph Theory, Jo Martin, Puck Rombach; arXiv:2009.04529, 2020.
Guessing Numbers of Odd Cycles, Ross Atkins, Puck Rombach, Fiona Skerman; Electronic Journal of Combinatorics, 24(1), 2017.

Forbidden Induced Subgraphs
Role colouring graphs in hereditary classes, Christopher Purcell, Puck Rombach; arXiv:1802.10180, 2019.
On the complexity of role colouring planar graphs, trees and cographs, Christopher Purcell, Puck Rombach; Journal of Discrete Algorithms, 35, 2015.

Complex Networks and Data Science
A guide to choosing and implementing reference models for social network analysis, Elizabeth A. Hobson, Matthew J. Silk, Nina H. Fefferman, Daniel B. Larremore, Puck Rombach, Saray Shai, Noa Pinter-Wollman; arXiv:2012.04720, 2020.
Core-periphery structure in networks (revisited), Puck Rombach, Mason A. Porter, James H. Fowler, Peter J. Mucha; SIAM Review, 59(3), 2017.
Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths, Mihai Cucuringu, Puck Rombach, Sang Hoon Lee, Mason A. Porter; European Journal of Applied Mathematics, 27(6), 2016. 
Pursuit on an organized crime network, Charles Z. Marshak, Puck Rombach, Andrea L. Bertozzi, Maria R. D'Orsogna; Physical Review E, 93(022308), 2015.
Core-Periphery Structure in Networks, Puck Rombach, Mason A. Porter, James H. Fowler, Peter J. Mucha; SIAM Journal on Applied Mathematics, 74(1), 2014.
Discriminating Power of Centrality Measures, Puck Rombach, Mason Porter; arXiv:1305.3146, 2013.
Task-Based Core-Periphery Organization of Human Brain Dynamics, Danielle S. Bassett, Nicholas F. Wymbs, Puck Rombach, Mason A. Porter, Peter J. Mucha, Scott T. Grafton; PLoS Computational Biology, 9(9)2013.

Outreach
Commentary: Teach Network Science to Teenagers, Heather A. Harrington, Mariano Beguerisse-Díaz, Puck Rombach, Laura M. Keating, Mason A. Porter; Network Science, 1(2), 2013. (Teaching materials are available here.)