Department of Mathematics
My research interests are graph theory and combinatorics. My current research falls primarily into two categories — graph searching and surveillance (cops and robbers, eternal domination) and properties of graphs with forbidden induced subgraphs. I have also conducted research in graph colouring and labelling, cycles in graphs (in particular, Hamiltonian cycles and cycle extendibility), extremal graph theory, and computational geometry.
I hold an appointment as an adjunct researcher (professeur associé) in the Département d’informatique et de recherche opérationnelle at the l’Université de Montréal. I am also a member of the Centre de Recherches Mathématiques.
- PhD (Applied Mathematics), Carleton University, 2012.
Thesis: Derived Colourings of Graphs
Supervisor: Brett Stevens
- M.Math (Combinatorics & Optimization), University of Waterloo, 2005.
Thesis: Sheehan’s Conjecture and Parity Results on Regular, Hamiltonian Graphs
- B.Sc Hon (Mathematics), Mount Allison University, 2003.
Selected Grants & Awards
NSERC Discovery Grant, How do forbidden induced subgraphs impact global phenomena in graphs?, Université de Montréal, 2017–2022.
- FRQNT Research grant (Programme de recherche pour les enseignants de collége), New directions in the “cops and robbers” graph searching model, Dawson College, 2017–2020.
- FRQNT Research grant (Programme de recherche pour les enseignants de collége), A study on path and cycle based properties of graphs, Dawson College, 2014–2018.
NSERC Postdoctoral Fellowship, Université de Montréal, 2012–2014.
On uniquely Hamiltonian claw-free and triangle-free graphs, Discuss. Math. Graph Theory, 35:2 (2015), 207–214.
- Sequence variations of the 1-2-3 Conjecture and irregularity strength. Discrete Math. Theor. Comput. Sci., 15:1 (2013), 15–28 (with B. Stevens).
- Vertex-colouring edge-weightings with two edge weights. Discrete Math. Theor. Comput. Sci., 14:1 (2012), 1–20 (with M. Khatirinejad, R. Naserasr, M. Newman, B. Stevens).
- Spanning Trees with Specified Differences in Cayley Graphs. Discrete Math., 312:17 (2012), 2561–2565 (with B. Stevens).
- π/2-Angle Yao Graphs are Spanners. Internat. J. Comput. Geom. Appl., 22:1 (2012), 61-82 (with P. Bose, M. Damian, K. Douïeb, J. O’Rourke, M. Smid, S. Wuhrer).
The 1-2-3 Conjecture and related problems: a survey (unpublished), preprint (2012).
- Digraphs are 2-weight choosable. Electron. J. Combin., 18 (2011), #P21 (with M. Khatirinejad, R. Naserasr, M. Newman, B. Stevens).
- π/2-Angle Yao Graphs are Spanners. Algorithms and Computation, Part II, 446–457 (2010), Lecture Notes in Comput. Sci., 6507, Springer, Berlin (with P. Bose, M. Damian, K. Douïeb, J. O’Rourke, M. Smid, S. Wuhrer).
Independent dominating sets and hamiltonian cycles. J. Graph Theory, 54:3 (2007), 233-244 (with P. Haxell, J. Verstraete).
Conference and Workshop Presentations
Edge clique covers in graphs with independence number 2, 4th Bordeaux Graph Workshop, Université de Bordeaux, France (2016).
Introduction to graph colouring, AMQ Summer Camp, Dawson College (2016).
Fully active cops and robbers, 5th Graph Searching in Canada Workshop, Dalhousie University (2016).
On Hendry’s Conjecture: Extending cycles in chordal graphs, Mathematics Department Seminar, Dawson College (2015).
Probabilistic methods in discrete mathematics: the Lovasz Local Lemma and Ramsey numbers, Mathematics Department Seminar, Dawson College (2015).
Hendry’s Conjecture: counterexamples and new open problems, 5th Canadian Discrete and Algorithmic Mathematics Conference, University of Saskatchewan (2015).
Hamiltonian chordal graphs are not cycle extendible, 9th International Colloquium on Graph Theory and Combinatorics, Université Joseph Fourier, Grenoble, France (2014).
Cycle extendibility in Hamiltonian chordal graphs, Graphs @ Ryerson Seminar, Ryerson University (2014).
Forbidden subgraphs and sufficient conditions for cycle extendibility in graphs, 4th Canadian Discrete and Algorithmic Mathematics Conference, Memorial University of Newfoundland (2013).
A general bound on the weight choosability number of a graph, 4th Canadian Discrete and Algorithmic Mathematics Conference, Memorial University of Newfoundland (2013).
Bounding a graph’s weight choosability, Carleton-Ottawa Discrete Mathematics Seminar, Carleton University (2012).
Colourings Derived from Weightings, 23rd British Combinatorial Conference, University of Exeter, UK (2011).
Variations of the 1,2,3-Conjecture, 3rd Canadian Discrete and Algorithmic Mathematics Conference, University of Victoria (2011).
Graph colourings derived from graph weightings, Discrete Math Days, University of Ottawa (2011).
Spanning Trees with Specified Differences in Cayley Graphs, 8th French Combinatorial Conference, Université de Paris XI – Sud, Orsay, France (2010).
Spanning Trees with Specified Differences in Cayley Graphs, Society of Industrial and Applied Mathematics (SIAM) Conference on Discrete Mathematics, University of Texas (2010).
Edge weightings that induce proper vertex colourings, Discrete Math Days, Carleton University (2009).
Graph Spanners, Department of Computer Science Algorithms Seminar, Carleton University (2009).
- Aaron Krim-Yee, 2017–present
FRQNT Bourses de stages d’été pour les étudiants de niveau collégial (Summer 2017)
- Jerry Huang, Summer 2017
- Alexander Hassler (Dawson College), 2016–2017
FRQNT Bourses de stages d’été pour les étudiants de niveau collégial (Summer 2016)
- Ilya Gromovikov (Dawson College), 2014–2015
Université de Montréal
- Virgile Virgélot (M.Sc.), 2017–present
- Alizée Gagnon (B.Sc.), Summer 2016 & Summer 2017
- Fionn Mc Inerney (PhD, Université Côte d’Azur, France), Summer 2017
- Andrés Mejía Zacarías (B.Sc., Universidad Nacional Autónoma De México, México), Summer 2017
MITACS Globalink Research Internship
- Rezvan Sherkati (B.Sc., Sharif Univeristy of Technology, Iran), Summer 2015
- Valentin Giboulot (B.Sc., Université Blaise Pascal Clermont-Ferrand, France), Summer 2013
Past and Present Collaborators
Laurent Beaudou | Prosenjit Bose | Pierre Charbit | Nancy Clarke | Mirela Damian | Karim Douïeb | Gena Hahn | Penny Haxell | Marcin Kamiński | Mahdad Khatirinejad | Bill Kinnersley | Manuel Lafond | Nicolas Lichiardopol | Reza Naserasr | Mike Newman | Kerry Ojakian | Joseph O’Rourke | Rezvan Sherkati | Michiel Smid | Brett Stevens | Jacques Verstraete | Stefanie Wuhrer