puck.rombach

@uvm.edu

Research

I am an Associate Professor at the Department of Mathematics & Statistics and the Vermont Complex Systems Center at the University of Vermont. My main research interests are in structural and extremal graph theory, matroids, algorithms and complexity. I also enjoy interdisciplinary work and collaborations with NASA.
Previously, I was a post-doc at the University of California, Los Angeles, under Andrea Bertozzi. I received my D.Phil. from the University of Oxford, advised by Mason Porter and Alex Scott.
I am an organizer for the Graduate Research Workshop in Combinatorics, and editor for the American Journal of Combinatorics.

Students

Current: Calum Buchanan (PhD), Jeremy Quail (PhD), Per Wagenius (MS)

Former: Colin Levaunt (MS), Jo Martin (MS), Hunter Rehm (PhD)

Publications

  1. Ternary positroids, arXiv:2402.17841, 2024 (with Jeremy Quail)
  2. Positroid envelopes and graphic positroids, arXiv:2402.17841, 2024 (with Jeremy Quail)
  3. Canonizing graphs of bounded rank-width in parallel via Weisfeiler-Leman, arXiv:2306.17777, 2024 (with Michael Levet and Nicholas Sieger)
  4. A lower bound on the saturation number and a strengthening for triangle-free graphs, arXiv:2402.11387, 2024 (with Calum Buchanan)
  5. Path odd-covers of graphs, arXiv:2306.06487, 2023 (with Steffen Borgwardt, Calum Buchanan, Eric Culver, Bryce Frederickson and Youngho Yoo)
  6. Odd covers of graphs,  Journal of Graph Theory, 104(2):420-439, 2023 (with Calum Buchanan, Alexander Clifton, Eric Culver, Jiaxi Nie, Jason O’Neill and Mei Yin)
  7. On the last new vertex visited by a random walk in a directed graph, Discrete Mathematics Letters, 11:96–98, 2023 (with Calum Buchanan and Paul Horn)
  8. Generating dominating sets using locally-defined centrality measures, arXiv:2305.08218, 2023 (with Hunter Rehm and Robert Kassouf-Short)
  9. Toughness of recursively partitionable graphs, Theory and Applications of Graphs, 10(2), 2023 (with Calum Buchanan, Brandon Du Preez and K. E. Perry)
  10. Node placement to maximize reliability of a communication network with application to satellite swarms, 2023 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 3466-3473, 2023 (with Calum Buchanan, James Bagrow and Hamid Ossareh)
  11. The effect of the Katz parameter on node ranking, with a medical application, Social Network Analysis and Mining, 13:132, 2023 (with Hunter Rehm, Mona Matar and Lauren McIntyre)
  12. Subgraph complementation and minimum rank, Electronic Journal of Combinatorics, 29(1), 2022 (with Calum Buchanan and Christopher Purcell)
  13. Guessing numbers and extremal graph theory, Electronic Journal of Combinatorics, 29(2), 2022 (with Jo Martin)
  14. Rainbow saturation, Graphs and Combinatorics, 38(166), 2022 (with Neal Bushaw and Daniel Johnston)
  15. Distinguishing generalized Mycielskian graphs, Australasian Journal of Combinatorics, 83(2): 225–242, 2022 (with Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb and K. E. Perry)
  16. Symmetry parameters of various hypercube families, The Wilfried Imrich Issue of the Art of Discrete and Applied Mathematics, 2022 (with Debra Boutin, Sally Cockburn, Lauren Keough and Sarah Loeb)
  17. Symmetry parameters for Mycielskian graphs, Research Trends in Graph Theory and Applications, Springer, 2021, pp 99-117 (with Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb and K. E. Perry)
  18. Role colouring graphs in hereditary classes, Theoretical Computer Science, 876:12-24, 2021 (with Christopher Purcell)
  19. A guide to choosing and implementing reference models for social network analysis, Biological Reviews, 96(6):2716-2734, 2021 (with Elizabeth A. Hobson, Matthew J. Silk, Nina H. Fefferman, Daniel B. Larremore, Saray Shai and Noa Pinter-Wollman)
  20. Lower bounds for rainbow Turán numbers of paths and other trees, Australasian Journal of Combinatorics, 78(1), 2020 (with Daniel Johnston)
  21. Determining number and cost of generalized Mycielskian graphs, arXiv:2007.15284, 2020 (with Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb and K. E. Perry)
  22. Guessing numbers of odd cycles, Electronic Journal of Combinatorics, 24(1), 2017 (with Ross Atkins and Fiona Skerman)
  23. Core-periphery structure in networks (revisited), SIAM Review, 59(3), 2017 (with Mason A. Porter, James H. Fowler and Peter J. Mucha)
  24. Rank aggregation for course sequence discovery, In: Complex Networks & Their Applications VI, Studies in Computational Intelligence, 689, 2017 (with Charles Z. Marshak, Mihai Cucuringu and Dillon Montag)
  25. Detection of core-periphery structure in networks using spectral methods and geodesic paths, European Journal of Applied Mathematics, 27(6), 2016 (with Mihai Cucuringu, Sang Hoon Lee and Mason A. Porter)
  26. On the complexity of role colouring planar graphs, trees and cographs, Journal of Discrete Algorithms, 35, 2015 (with Christopher Purcell)
  27. Pursuit on an organized crime network, Physical Review E, 93(022308), 2015 (with Charles Z. Marshak, Andrea L. Bertozzi and Maria R. D’Orsogna)
  28. Core-periphery structure in networks, SIAM Journal on Applied Mathematics, 74(1),2014 (with Mason A. Porter, James H. Fowler and Peter J. Mucha)
  29. Task-based core-periphery organization of human brain dynamics, PLoS Computational Biology, 9(9), 2013 (with Danielle S. Bassett, Nicholas F. Wymbs, Mason A. Porter, Peter J. Mucha and Scott T. Grafton)
  30. Commentary: Teach network science to teenagers, Network Science, 1(2), 2013 (with Heather A. Harrington, Mariano Beguerisse-Díaz, Laura M. Keating and Mason A. Porter)

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