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Dr. Christopher Duffy
(Phd: UVic/BdxU 2015)
Assistant Professor (tenure track)
Department of Mathematics and Statistics
University of Saskatchewan, Canada
firstname.lastname@usask.ca

Recent Activities (current to August 2019)
-Attended and presented at the 16th International Workshop for Algorithms and Models for the Web Graph (August 2019  -- Brisbane, Australia)
-Presented at the Walter Murray Collegiate Math Camp (July 2019 -- Saskatoon, Canada)
-Attended and presented at the 7th biennial Canadian Discrete and Algorithmic Mathematics Conference (June 2019 -- Vancouver, Canada)
-Organized a minisymposium in graph polynomials for the CMS Winter Meeting (June 2019  -- Vancouver, Canada)
-Research visit to the University of Victoria (June 2019 -- Victoria, Canada)
-Awarded five-year grant from the National Science and Engineering Research Council for project Combinatorics of Mixed Graphs -- Homomorphism and Complexity (May 2019)
-Supervised a team in the COMAP Contest in Modeling (January 2019 -- Saskatoon, Canada)
-Research meeting with colleagues from Loughbrough  University (UK) (January 2019 -- Saskatoon, Canada)
-Attended and presented at the CMS Winter Meeting (December 2018  -- Vancouver, Canada)
-Research meeting with colleages at Mount Saint Vincent University  (November 2018 -- Halifax, Canada)
-Invited lecture at Mount Saint Vincent University Dept. of Mathematics Colloquium
(November 2018 -- Halifax, Canada)
-Invited lecture at University of Saskatchewan Math Club (November 2018 -- Saskatoon, Canada)


Research Interests
My research interests lie primarily in algorithmic and computational aspects of graph theory,  particularly for problems defined on directed, signed and mixed graphs.  This includes applications in areas as wide ranging as quantum physics and social sciences. Within this framework I study homomorphisms and colourings, discrete-time processes and graph-searching models.  In each of these areas I utilize tools from discrete mathematics, combinatorics and theoretical computer science to study computational questions such as asymptotic behaviours of evolving discrete systems, parameter bounds, and computational complexity. My research yields fundamental theorems and analyses that lay the groundwork for  future applications of multi-layer graph models in the social and physical sciences.


As is standard in the field, author order is alphabetical on all contributions below.
Refereed Contributions
1. Duffy C, MacGillivray G, Raspaud A. (2014). Oriented Incidence Colouring of Digraphs. Bordeaux Graph Workshop 2014, Bordeaux, France (14-18)
2. Duffy C, MacGillivray G. (2015). An Analysis of the Weighted Firefighter Problem. Journal of Combinatorial Computing and Combinatorial Mathematics. 94: 167-175.
3. Duffy C, Janssen J. (2016).  The Spread of Cooperative Strategies on Grids with Random Asynchronous Updating Lecture Notes in Computer Science 10088: The 13th International Workshop for Algorithms and Models for the Web Graph, (152-163)
4. Duffy C, MacGillivray G, Sopena E. (2016). A Study of k-dipath Colourings of Digraphs. Bordeaux Graph Workshop 2016, Bordeaux, France (124-128)
5. Bensmail J, Duffy C, Sen S. (2017). An Analogue of Clique for (m,n)-mixed Colored Graphs. Graphs and Combinatorics. 33(4): 735-750.
6. Bard S, Duffy C, Edwards M, MacGillivray G, Yang F. (2017). Eternal Domination in Split Graphs. Journal of Combinatorial Computing and Combinatorial Mathematics. 101: 121-130.
7. Duffy C, Janssen J. (2017). The Spread of Cooperative Strategies on Grids with Random Asynchronous Updating. Internet Mathematics. 1(1) 10pp
8. Duffy C, Janssen J. (2018) Infinite n-ordered Graphs and Independent Distinguishing Sets. 10 International Colloquium on Graph Theory and Combinatorics, Lyon, France (#57 10pp)
9. Duffy C, Lidbetter TF, Messinger ME, Nowakowski R. (2018). A Variation on Chip-Firing: the diffusion game. Discrete Mathematics and Theoretical Computer Science. 20(1): #4
10. Duffy C, MacGillivray G, Sopena E. (2018). A Study of k-dipath Colourings of Oriented Graphs. Discrete Mathematics and Theoretical Computer Science. 20(1): #6
11. Bard S, Bellitto T, Duffy C, MacGillivray G, Yang F. (2018). Complexity of Locally Injective Homomorphism to Tournaments. Discrete Mathematics and Theoretical Computer Science. 20(2): #4
12. Duffy C, MacGillivray G, Ochem P, Raspaud A. (2019). Oriented Incidence Colourings of Digraphs. Discussiones Mathematicae Graph Theory. 39(1): 191-210
13. Duffy C, MacGillivray G, Sopena E (2019). Oriented Colourings of Bounded Degree Graphs. Discrete Mathematics. 342(4):959-97$
14. Duffy C, MacGillivray G. (2019). Firefighter -- Saving Sets of Vertices on Cubic Graphs. Networks. 74(1):62-69
15. Duffy C, Janssen J. (2019).  Constructing Infinite n-ordered Graphs Lecture Notes in Computer Science 11631: The 16th International Workshop for Algorithms and Models for the Web Graph, (44-56)
16. Cox D, Duffy C (2019). The Oriented Chromatic Polynomial Electronic Journal of Combinatorics. (to appear)

Preprints
1. Clarke NE, Cox D, Duffy C, Dyer D, Fiztpatrick S, Messinger ME (2018). Limited Visibility Cops and Robbers. (Under review, revision requested) (preprint)
2. Barrett J, Duffy C, Nowakowski R (2019). The Spread of Voting Attitudes in Social Networks (Under review, revision requested) (preprint)
3. Duffy C, Pas J (2019). The Simple Chromatic Number of Oriented Graphs (preprint)
4. Duffy C (2019). A Note on Colourings of Connected Oriented Cubic Graphs (preprint)

Student Research and Supervision
R. Cutcliffe The Prisoners Dilemma on Graphs (2016) Undergraduate Honours Thesis,  Dalhousie University, co-supervised with Dr. J. Janssen
J. Barrett The Power Index Game (2016) NSERC USRA, Dalhousie University, co-supervised with Dr. R. Nowakowski

J. Barrett The Power Index Game (2016) Undergraduate Honours Thesis, Dalhousie University,  co-supervised with Dr. R. Nowakowski

J. Pas The Simple Chromatic Polynomial (2018), Undergraduate Student Research, University of Saskatchewan

S. Shan Bootstrap Processes in Digraphs (2019) Undergraduate Student Research, University of Saskatchewan

J. Mitchell Universal Adjacency Properties in Mixed Graphs (2019) Undergraduate Student Research, University of Saskatchewan

N. Zolkovich Chromatic Polynomials of Directed Graphs (2019) Undergraduate Student Research, University of Saskatchewan

T. Black Continuous and Discrete Mathematical Modeling of Metal Additive Manufacturing Processes (2019) NSERC USRA  co-supervised with Dr. A. Cheviakov



Past Employment
2015 - 2017, Postdoctoral Scholar, Department of Mathematics and Statistics, Dalhousie University, Canada
2015 - 2017, Outreach Coordinator, Atlantic Association for Research in the Mathematical Sciences, Canada
2011 - 2015, Sessional Instructor,  Department of Mathematics and Statistics, Univeristy of Victoria, Canada