Research



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Submitted Preprints

  1. Critical (P5, W4)-free graphs, January 2025 (with Wen Xia, Jorik Jooken, Jan Goedgebeur, Iain Beaton, and Shenwei Huang) [arXiv]
  2. Vertex-critical graphs in co-gem-free graphs, October 2024 (with Iain Beaton) [arXiv]
  3. An approximation algorithm for zero forcing, February 2024 (with Jeannette Janssen, Rogers Matthew, and Zhiyuan Zhang*) [arXiv]

Publications

  1. Cut-Down de Bruijn Sequences Discrete Mathematics 348:114204 (2025) (with Aysu Gündoğan* and Joe Sawada) [DOI] [arXiv]
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. The node cop-win reliability of unicyclic and bicyclic graphs, Networks 79(2): 189-201 (2022) (with Maimoonah Ahmed*) [DOI] [arXiv]
  11. 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]
  12. A note on purely imaginary independence roots, Discrete Mathematics 343(12): 112113 (2020) (with Jason Brown) [DOI] [arXiv]
  13. 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)]
  14. Independence equivalence classes of paths and cycles, Australasian Journal of Combinatorics 75(1): 127-145 (2019) (with Jason Brown and Iain Beaton) [Open access]
  15. On the unimodality of independence polynomials of very well-covered graphs, Discrete Mathematics 341(4): 1138-1143 (2018) (with Jason Brown) [DOI] [arXiv]
  16. On the Stability of Independence Polynomials, The Electronic Journal of Combinatorics 25#P1.46 18pp. (2018) (with Jason Brown) [Open access]
  17. 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. 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]
  2. 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]
  3. 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]
  4. 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]
  5. Vertex-critical (P3+ℓP1)-free graphs Coast Combinatorics Conference 2023, Simon Fraser University, Vancouver, BC, March 2023 [slides]
  6. The node cop-win reliability of unicyclic and bicyclic graphs GRASCan2022, Virtual, August 2022 [slides]
  7. Classifying H-free critical graphs Prairie Discrete Mathematics Workshop 2022 Lightning Talk, Virtual, June 2022
  8. The largest real root of the independence polynomial of a unicyclic graph CanaDAM2021 Graph Polynomials Minisymposium, Virtual, May 2021 [slides]
  9. The mean subtree order of a graph under edge addition CMS Winter Meeting Graph Theory Session, Virtual, December 2020 [slides]
  10. Families of graphs containing only finitely many vertex-critical graphs Atlantic Graph Theory Seminar Virtual, October 2020 [video]
  11. 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
  12. Independence Equivalence Classes of Paths and Cycles Graphs@Ryerson Seminar, Ryerson University, Toronto, ON, February 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. Shannon Fitzpatrick
  8. Jan Goedgebeur
  9. Aaron Grubb* (x2)
  10. Aysu Gündoğan*
  11. Chính Hoàng (x4)
  12. Shenwei Huang
  13. Jeannette Janssen
  14. Jorik Jooken
  15. Thaler Knodel*
  16. Rogers Matthew
  17. Lucas Mol
  18. Joe Sawada (x7)
  19. Aaron Williams (x2)
  20. Wen Xia
  21. Zhiyuan Zhang*

* indicates coauthor is/was my student