Research



Home Research Teaching

To see my research on a specific topic, click the appropriate button!

Submitted Preprints

  1. On Gyárfás' Path-Colour Problem, June 2025 (with Alexander Clow) [arXiv]
  2. An approximation algorithm for zero forcing, February 2024 (with Jeannette Janssen, Rogers Matthew, and Zhiyuan Zhang*) [arXiv]

Accepted Preprints

  1. Critical (P5, W4)-free graphs, to appear in COCOON 2025 (with Wen Xia, Jorik Jooken, Jan Goedgebeur, Iain Beaton, and Shenwei Huang) [arXiv]

Publications

  1. Vertex-critical graphs in co-gem-free graphs, Theoretical Computer Science 1042:115234 (2025) (with Iain Beaton) [Open Access] [arXiv]
  2. Cut-Down de Bruijn Sequences, Discrete Mathematics 348:114204 (2025) (with Aysu Gündoğan* and Joe Sawada) [DOI] [arXiv]
  3. A Tight Upper Bound on the Average Order of Dominating Sets of a Graph, Journal of Graph Theory 107(3):463-477 (2024) (with Iain Beaton) [Open Access]
  4. Pivot Gray codes for the spanning trees of a graph ft the Fan, Graphs and Combinatorics 40:78 (2024) (with Aaron Grubb* and Joe Sawada) [DOI] [arXiv]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. The node cop-win reliability of unicyclic and bicyclic graphs, Networks 79(2): 189-201 (2022) (with Maimoonah Ahmed*) [DOI] [arXiv]
  12. 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]
  13. A note on purely imaginary independence roots, Discrete Mathematics 343(12): 112113 (2020) (with Jason Brown) [DOI] [arXiv]
  14. 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)]
  15. Independence equivalence classes of paths and cycles, Australasian Journal of Combinatorics 75(1): 127-145 (2019) (with Jason Brown and Iain Beaton) [Open access]
  16. On the unimodality of independence polynomials of very well-covered graphs, Discrete Mathematics 341(4): 1138-1143 (2018) (with Jason Brown) [DOI] [arXiv]
  17. On the Stability of Independence Polynomials, The Electronic Journal of Combinatorics 25#P1.46 18pp. (2018) (with Jason Brown) [Open access]
  18. Edge contraction and cop-win critical graphs, Australasian Journal of Combinatorics 63(1): 70-87 (2015) (with Shannon Fitzpatrick) [Open access]

Conference Proceedings

  1. On the finiteness of k-vertex-critical 2P2-free graphs with forbidden induced squids or bulls, IWOCA2024: Proceedings from the 35th International Workshop on Combinatorial Algorithms, LNCS 14764: 301-313 (2024) (with Melvin Adekanye*, Christopher Bury*, and Thaler Knodel*) [DOI] [arXiv] [critical graph files]
  2. 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]
  3. 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]

Talks (last 5 years)

  1. Critical (P5, W4)-free graphs, GO XII, Haute Ecole de Santé - Filiére Physiothérapie, Leukerbad, Switzerland, July 2025 ***Upcoming!***
  2. Critical (P5, W4)-free graphs, CanaDAM 2025, Structured Families of Graphs and Digraphs: Classic and New Problems University of Ottawa, Ottawa, ON, May 2025 [slides]
  3. Vertex-critical graphs in co-gem-free graphs, CMS Winter Meeting Graph Structure and Algorithms Session, Kwantlen Polytechnic University, Richmond Campus, Richmond, BC, December 2024 [slides]
  4. Efficient certifying algorithms for k-colouring subfamilies of P5-free graphs, ISMP 2024, Complexity and algorithmic aspects of structured families of graphs Stream Palais des congrès de Montréal, Montréal, QC, July 2024 [slides]
  5. 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 [slides]
  6. A finite and an infinite family of k-critical (P5, H)-free graphs, CanaDAM 2023, Graph Structure: Algorithms and Complexity Minisymposium University of Winnipeg, Winnipeg, MB, June 2023 [slides]
  7. Vertex-critical (P3+ℓP1)-free graphs , Coast Combinatorics Conference 2023, Simon Fraser University, Vancouver, BC, March 2023 [slides]
  8. The node cop-win reliability of unicyclic and bicyclic graphs, GRASCan2022, Virtual, August 2022 [slides]
  9. Classifying H-free critical graphs, Prairie Discrete Mathematics Workshop 2022 Lightning Talk, Virtual, June 2022
  10. The largest real root of the independence polynomial of a unicyclic graph CanaDAM2021 Graph Polynomials Minisymposium, Virtual, May 2021 [slides]
  11. The mean subtree order of a graph under edge addition, CMS Winter Meeting Graph Theory Session, Virtual, December 2020 [slides]
  12. Families of graphs containing only finitely many vertex-critical graphs, Atlantic Graph Theory Seminar Virtual, October 2020 [video]
  13. 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

Theses

Coauthors in alphabetical order by last name:

  1. Tala Abuadas
  2. Melvin Adekanye*
  3. Maimoonah Ahmed*
  4. Iain Beaton (x5)
  5. Jason Brown (x5)
  6. Christopher Bury*
  7. Alexander Clow
  8. Shannon Fitzpatrick
  9. Jan Goedgebeur
  10. Aaron Grubb* (x2)
  11. Aysu Gündoğan*
  12. Chính Hoàng (x4)
  13. Shenwei Huang
  14. Jeannette Janssen
  15. Jorik Jooken
  16. Thaler Knodel*
  17. Rogers Matthew
  18. Lucas Mol
  19. Joe Sawada (x7)
  20. Aaron Williams (x2)
  21. Wen Xia
  22. Zhiyuan Zhang*

* indicates coauthor is/was my student