Puck Rombach

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.

Graduate Research Students

Calum Buchanan, Jo Martin (MS thesis), Colin Giles,  Jeremy Quail,  Hunter Rehm

Publications

Toughness of recursively partitionable graphs, Calum Buchanan, Brandon Du Preez, K. E. Perry, Puck Rombach; arXiv:2210.10590, 2022.
The effect of the Katz parameter on node ranking, with a medical application, Hunter Rehm, Mona Matar, Puck Rombach, Lauren McIntyre; arXiv:2210.06392, 2022.
Rainbow Saturation, Neal Bushaw, Daniel Johnston, Puck Rombach; Graphs and Combinatorics, 38(166), 2022.
On the last new vertex visited by a random walk in a directed graph, Calum Buchanan, Paul Horn, Puck Rombach; arXiv:2209.08079, 2022.
Odd covers of graphs, Calum Buchanan, Alexander Clifton, Eric Culver, Jiaxi Nie, Jason O'Neill, Puck Rombach, Mei Yin; arXiv:2202.09822, 2022.
Subgraph complementation and minimum rank, Calum Buchanan, Christopher Purcell, Puck Rombach; Electronic Journal of Combinatorics, 29(1), 2022.
Guessing Numbers and Extremal Graph Theory, Jo Martin, Puck Rombach; Electronic Journal of Combinatorics, 29(2), 2022.
Distinguishing Generalized Mycielskian Graphs, Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach; Australasian Journal of Combinatorics, 83(2): 225–242, 2022.
Role colouring graphs in hereditary classes, Christopher Purcell, Puck Rombach; Theoretical Computer Science, 876:12-24, 2021.
Symmetry Parameters of Various Hypercube Families, Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, Puck Rombach; The Wilfried Imrich Issue of the Art of Discrete and Applied Mathematics, 2022.
Symmetry Parameters for Mycielskian Graphs, Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach; Research Trends in Graph Theory and Applications, Springer, 2021, pp 99-117.
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; Biological Reviews, 96(6):2716-2734, 2021.
Lower bounds for rainbow Turán numbers of paths and other trees, Daniel Johnston, Puck Rombach; Australasian Journal of Combinatorics, 78(1), 2020.
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.
Guessing Numbers of Odd Cycles, Ross Atkins, Puck Rombach, Fiona Skerman; Electronic Journal of Combinatorics, 24(1), 2017.
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. 
On the complexity of role colouring planar graphs, trees and cographs, Christopher Purcell, Puck Rombach; Journal of Discrete Algorithms, 35, 2015.
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.
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.)