Assistant Professor at the Department of Mathematics and Statistics, University of Vermont.
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.
Lower bounds for rainbow Turán numbers of paths and other trees, Daniel Johnston, Puck Rombach; Australasian Journal of Combinatorics, 78(1), 2020.
Rainbow Saturation, Neal Bushaw, Daniel Johnston, Puck Rombach; arXiv:2003.13200, 2020.
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.
Expressing graphs as symmetric differences of cliques of the complete graph, Calum Buchanan, Christopher Purcell, Puck Rombach; arXiv:2101.06180, 2021.
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.
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.
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.
Rank Aggregation for Course Sequence Discovery, Charles Z. Marshak, Mihai Cucuringu, Dillon Montag and Puck Rombach; In: Complex Networks & Their Applications VI, Studies in Computational Intelligence, vol 689., 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.
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.