I am a graph theorist, broadly interested in colouring and structure, among other things. My research has been supported by grants from the Simons Foundation (award #845698, 2021-2026), the National Science Foundation (award NSF-DMS-1600551, 2016-2019), and the AU Intramural Grants Program (2020-2021, 2014-2015).

I am on the Editorial Board of the journal Graphs and Combinatorics.

I regularly teach courses from the following list:

• Math 5750/6750/7700/7750/7970 (Graph Theory and Advanced Topics in Graph Theory)
• Math 5710/6710 (Linear Optimization)
• Math 5730/6730 (Enumeration)
• Math 3100 (Introduction to Advanced Math)

I have received several departmental teaching awards: the Robert K. Butz Award (2013); the Marie Kraska Award (2019), and the Outstanding Teacher of Graduate Students Award (2021).

• R. Galindo and J. McDonald, On graphs with chromatic number and maximum degree both equal to nine, submitted. [arXiv]
• A. Dalal, J. McDonald and S. Shan, A reduction of the "cycles plus K4's problem", submitted. [arXiv]
• O. Henderschedt and J. McDonald, On orientations with forbidden outdegrees, submitted. [arXiv]
• A. Dalal, J. McDonald and S. Shan, Total coloring graphs with large maximum degree, submitted. [arXiv]
• A. Jimenez, J. McDonald, R. Naserasr, K. Nurse and D. Quiroz, Balanced-chromatic number and Hadwiger-like conjectures, submitted. [arXiv]
• A. Brewer Castano, J. McDonald and K. Nurse, Group connectivity in 3-edge-connected signed graphs, accepted by SIAM Journal on Discrete Math. [arXiv]
• M. DeVos, J. McDonald and K. Nurse, Another proof of Seymour's 6-flow theorem, Journal of Graph Theory 106 (2024) 944-946. [arXiv][Journal]
• K. Collins, M. Heenehan and J. McDonald, A Note on the Immersion Number of Generalized Mycielski Graphs, in: Combinatorics, Graph Theory and Computing: SEICCGTC 2021, Springer Proceedings in Mathematics & Statistics (eds. F. Hoffman et al.) 448 (2024), 235-243. [arXiv][Publisher]
• J. Harrelson and J. McDonald, List-edge-colouring triangulations with maximum degree at most five, Australasian Journal of Combinatorics 88 (2024), 127-143.  [arXiv][Journal]
• K. Collins, M. Heenehan and J. McDonald, Clique immersion in graph products, Discrete Mathematics 346 (2023), 113421. [arXiv] [Journal]
• J. McDonald and G. Puleo, Strong coloring 2-regular graphs: cycle restrictions and partial colorings, Journal of Graph Theory 100 (2022), 653-670. [arXiv][Journal]
• G. Araujo-Pardo, Z. Berkkyzy, J. Faudree, K. Hogenson, R. Kirsch, L. Lesniak, J. McDonald, Finding Long Cycles in Balanced Tripartite Graphs: A First Step, in: Research Trends in Graph Theory and Applications, Association for Women in Mathematics Series (eds. Daniela Ferrero et al.), Springer, 2021. [Publisher]
• E. Krop, J. McDonald and G. Puleo, Upper bounds for inverse domination in graphs, Theory and Applications of Graphs 8 (2021), article 5 (9 pages). [arXiv] [Journal]
• M. Guyer and J. McDonald, On clique immersions in line graphs, Discrete Math. 343 (2020), article 112095 (7 pages) [arXiv][Journal]
• J. McDonald, G. Puleo and C. Tennenhouse, Packing and Covering Directed Triangles, Graphs and Combinatorics 36 (2020), 1059-1063. [arXiv] [Journal]
• J. McDonald and G. Puleo. t-Cores for (\Delta+t)-edge-colouring, Journal of Graph Theory 95 (2020), 165-180. [arXiv] [Journal]
• M. DeVos, J. McDonald, I. Pivotto, E. Rollova and R. Samal. 3-Flows with Large Support, Journal of Combinatorial Theory, Series B 144 (2020), 32-80. [arXiv] [Journal]
  
• M. DeVos, J. McDonald and A. Montejano, Non-monochromatic triangles in a 2-edge-coloured graph, Electronic Journal of Combinatorics 26 (2019), P3.8 (10 pages). [arXiv][Journal]
• J. Harrelson, J. McDonald and G. Puleo, List-edge-colouring planar graphs with precoloured edges, European Journal of Combinatorics 75 (2019), 55-65. [arXiv] [Journal]
• J. McDonald and G. Puleo, The list chromatic index of simple graphs whose odd cycles intersect in at most one edge, Discrete Math. 341 (2018), 713-722. [arXiv] [Journal]
• D. Hoffman, P. Johnson, J. McDonald and M. Noble, Application of an extremal result of Erdos and Gallai to the (n,k,t) problem, Theory and Applications of Graphs 4 (2017), article 1 (6 pages). [Journal]
• M. DeVos, J. McDonald and I. Pivotto, Packing Steiner Trees,  Journal of Combinatorial Theory, Series B 119 (2016), 178-213. [arXiv] [Journal]
• J. Asplund and J. McDonald, On a limit of the method of Tashkinov trees for edge-colouring, Discrete Math. 339 (2016), 2231-2238. [arXiv] [Journal]
• J. McDonald. Edge-colourings, in: Topics in Chromatic Graph Theory (eds. L. W. Beineke and R. J. Wilson), Cambridge University Press, 2015. [Publisher]
• D. Hoffman, P. Johnson and J. McDonald, Minimum (n,k,t) clique graphs, Congressus Numerantium 223 (2015), 199-204.
  
• M. DeVos, Z. Dvorak, J. Fox, J. McDonald, B. Mohar and D. Scheide, A minimum degree condition forcing complete graph immersion, Combinatorica 34 (2014), 279-298. [arXiv] [Journal]
• G. Chapuy, M. DeVos, J. McDonald, B. Mohar and D. Scheide, Packing triangles in weighted graphs, SIAM J. Discrete Math. 28 (2014), 226-239. [Journal]
• P. Johnson and J. McDonald, Note on the inverse domination number problem, Congressus Numerantium 215 (2013), 47-51.
• M. DeVos, J. McDonald, B. Mohar, and D. Scheide, A note on forbidding clique immersions, Electronic Journal of Combinatorics 20 (2013), #P55 (5 pages). [Journal]
• M. DeVos, J. McDonald, and D. Scheide, Average degree in graph powers, Journal of Graph Theory 72 (2013): 7-18. [arXiv] [Journal]
• M. DeVos, J. McDonald, B. Mohar and D. Scheide, Immersing complete digraphs, European Journal of Combinatorics 33 (2012), 1294-1302. [arXiv] [Journal]
• J. McDonald, B. Mohar, D. Scheide, Kempe equivalence of edge-colourings in subcubic and subquartic graphs, Journal of Graph Theory 70 (2012), 226-239. [arXiv] [Journal]
• P. Haxell and J. McDonald, On Characterizing Vizing's Edge-Colouring Bound, Journal of Graph Theory 69 (2012), 160-168. [Journal]
• J. M. McDonald, On a Theorem of Goldberg, Journal of Graph Theory 68 (2011), 8-21. [Journal]
• J. M. McDonald, On multiples of simple graphs and Vizing's Theorem, Discrete Math, 310 (2010), 2212-2214. [Journal]
• J. M. McDonald, Achieving maximum chromatic index in multigraphs, Discrete Math. 309 (2009), 2077-2084. [Journal]

The last three papers above contain results from my PhD thesis, which is available in full on the University of Waterloo's ethesis database.

• J. M. McDonald. Multigraphs with High Chromatic Index. PhD Thesis, University of Waterloo, 2009. [ethesis]