Research



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Submitted Preprints

  1. An approximation algorithm for zero frocing, February 2024 (with Jeannette Janssen, Rogers Matthew, and Zhiyuan Zhang*) [arXiv]
  2. Pivot Gray codes for the spanning trees of a graph ft the Fan, April 2023 (with Aaron Grubb* and Joe Sawada) [arXiv]
  3. A Tight Upper Bound on the Average Order of Dominating Sets of a Graph, November 2022 (with Iain Beaton) [arXiv]
  4. Cut-Down de Bruijn Sequences, May 2022 (with Aysu Gündoğan* and Joe Sawada) [arXiv]

Accepted Preprints

  1. On the finiteness of k-vertex-critical 2P2-free graphs with forbidden induced squids or bulls, to appear in IWOCA2024 (with Melvin Adekanye*, Christopher Bury*, and Thaler Knodel*) [arXiv]

Publications

  1. Infinite families of k-vertex-critical (P5, C5)-free graphs, Graphs and Combinatorics 40:30 (2024) (with Chính Hoàng) [DOI] [arXiv] [full-text journal version]
  2. Vertex-critical (P3+ℓP1)-free and vertex-critical (gem, co-gem)-free graphs, Discrete Applied Mathematics 344:179-187 (2024) (with Tala Abuadas, Chính Hoàng, and Joe Sawada) [DOI] [arXiv] [critical graph files]
  3. A refinement on the structure of vertex-critical (P5, gem)-free graphs, Theoretical Computer Science 961:113936 (2023) (with Chính Hoàng) [DOI] [arXiv] [code and critical graph files]
  4. Hamiltonicity of k-Sided Pancake Networks with Fixed-Spin: Efficient Generation, Ranking, and Optimality, Algorithmica 85:717-744 (2023) (with Joe Sawada and Aaron Williams) [DOI] [preprint]
  5. On the largest real root of the independence polynomial of a unicyclic graph, Open Journal of Discrete Applied Mathematics 5(3):30-46 (2022) (with Iain Beaton) [Open access] [arXiv]
  6. Dichotomizing k-vertex-critical H-free graphs for H of order four, Discrete Applied Mathematics 312(15): 106-115 (2022) (with Chính Hoàng and Joe Sawada) [DOI] [arXiv] [critical graph files] [a talk I gave on this Paper]
  7. The node cop-win reliability of unicyclic and bicyclic graphs, Networks 79(2): 189-201 (2022) (with Maimoonah Ahmed*) [DOI] [arXiv]
  8. On the Mean Subtree Order of Graphs Under Edge Addition, Journal of Graph Theory 96(3): 403-413 (2021) (with Lucas Mol) (This paper was a top cited article in the Journal of Graph Theory from 2021-22) [DOI] [arXiv]
  9. A note on purely imaginary independence roots, Discrete Mathematics 343(12): 112113 (2020) (with Jason Brown) [DOI] [arXiv]
  10. Maximum Modulus of Independence Roots of Graphs and Trees, Graphs and Combinatorics 36(3): 877-894 (2020) (with Jason Brown) [DOI] [arXiv] [journal version (view only)]
  11. Independence equivalence classes of paths and cycles, Australasian Journal of Combinatorics 75(1): 127-145 (2019) (with Jason Brown and Iain Beaton) [Open access]
  12. On the unimodality of independence polynomials of very well-covered graphs, Discrete Mathematics 341(4): 1138-1143 (2018) (with Jason Brown) [DOI] [arXiv]
  13. On the Stability of Independence Polynomials, The Electronic Journal of Combinatorics 25#P1.46 18pp. (2018) (with Jason Brown) [Open access]
  14. Edge contraction and cop-win critical graphs, Australasian Journal of Combinatorics 63(1): 70-87 (2015) (with Shannon Fitzpatrick) [Open access]

Conference Proceedings

  1. A Pivot Gray Code Listing for the Spanning Trees of the Fan Graph, COCOON 2021: Proceedings from 27th International Computing and Combinatorics Conference, LNCS 13025: 49-60 (2021) (with Aaron Grubb* and Joe Sawada) [DOI] [arXiv]
  2. A Hamilton Cycle in the k-Sided Pancake Network, IWOCA 2021: Proceedings from the 32nd International Workshop on Combinatorial Algorithms, LNCS 12757:137-151 (2021) (with Joe Sawada and Aaron Williams) [DOI] [arXiv] [C implementations of algorithms] [video of Joe's presentation]

Select Talks:

  1. On the finiteness of k-vertex-critical 2P2-free graphs with forbidden induced squids or bulls IWOCA 2024, Hotel Continental Terme, Ischia, Italy, July 2024 - *upcoming!*
  2. A finite and an infinite family of k-critical (P5, H)-free graphs CanaDAM 2023, University of Winnipeg, Winnipeg, MB, June 2023 [slides]
  3. Vertex-critical (P3+ℓP1)-free graphs Coast Combinatorics Conference 2023, Simon Fraser University, Vancouver, BC, March 2023 [slides]
  4. The node cop-win reliability of unicyclic and bicyclic graphs GRASCan2022, Virtual, August 2022 [slides]
  5. Classifying H-free critical graphs Prairie Discrete Mathematics Workshop 2022 Lightning Talk, Virtual, June 2022
  6. The largest real root of the independence polynomial of a unicyclic graph CanaDAM2021 Graph Polynomials Minisymposium, Virtual, May 2021 [slides]
  7. The mean subtree order of a graph under edge addition CMS Winter Meeting Graph Theory Session, Virtual, December 2020 [slides]
  8. Families of graphs containing only finitely many vertex-critical graphs Atlantic Graph Theory Seminar Virtual, October 2021 [video]
  9. Dichotomizing k-vertex-critical H-free graphs for H of order four AMS Fall Eastern Sectional Meeting Special Session on Combinatorics and Computing, Virtual (formerly Pennsylvania State University), October 2020
  10. Independence Equivalence Classes of Paths and Cycles Graphs@Ryerson Seminar, Ryerson University, Toronto, ON, February 2020
  11. The Maximum Modulus of an Independence Root CanaDAM 2019 Graph Polynomials Minisymposium, Simon Fraser University, Vancouver, BC, June 2019
  12. On the Stability of Independence Polynomials SIAM DM 2018 Graph Polynomials Minisymposium, University of Colorado, Denver, CO, June 2018
  13. The Independence Roots of a Graph East Coast Combinatorics Conference 2018, Dalhousie University, Halifax, NS, May 2018
  14. On the Unimodality of Independence Polynomials of Very Well-Covered Graphs CanaDAM 2017 Graph Polynomials Minisymposium, Ryerson University, Toronto, ON, June 2017
  15. Graph Properties, Polynomials, and Simplicial Complexes CMS Summer Meeting Graduate Student Research Session, University of Prince Edward Island, Charlottetown, PE, June 2015

Theses

Coauthors in alphabetical order by last name:

  1. Tala Abuadas
  2. Melvin Adekanye*
  3. Maimoonah Ahmed*
  4. Iain Beaton (x3)
  5. Jason Brown (x5)
  6. Christopher Bury*
  7. Shannon Fitzpatrick
  8. Aaron Grubb* (x2)
  9. Aysu Gündoğan*
  10. Chính Hoàng (x4)
  11. Jeannette Janssen
  12. Thaler Knodel*
  13. Rogers Matthew
  14. Lucas Mol
  15. Joe Sawada (x7)
  16. Aaron Williams (x2)
  17. Zhiyuan Zhang*

* indicates coauthor is/was my student