Ph.D., University of Waterloo, Canada
M.Math., University of Waterloo
B.Sc.H, Mount Allison University
Assistant Professor, Department of Mathematics and Statistics, Auburn University
2012 - present
NSERC Postdoctoral Fellow, Simon Fraser University
2010 - 2012
Research and Teaching Interests
I am a graph theorist, broadly interested in structure and colouring, among other things. My research is supported by a grant from the National Science Foundation, award NSF-DMS-1600551.
I regularly teach courses from the following list:
- Math 5750/6750/7700/7750/7970 (Graph Theory and Advanced Topics in Graph Theory)
- Math 3710/ Comp 3240 (Discrete Math/Discrete Structures)
- Math 5710/6710 (Linear Optimization)
- M. DeVos, J. McDonald, I. Pivotto, E. Rollova and R. Samal. 3-Flows with Large Support, submitted. [arXiv]
- J. McDonald and G. Puleo, The list chromatic index of simple graphs whose odd cycles intersect in at most one edge, submitted. [arXiv]
- D. Hoffman, P. Johnson, J. McDonald and M. Noble, Application of an extremal result of Erdos and Gallai to the (n,k,t) problem, submitted.
- L. Anderson, M. DeVilbiss, S. Holliday, P. Johnson, A. Kite, R. Matzke and J. McDonald. The edge Grundy numbers of some graphs, accepted by International Journal of Mathematics and Computer Science, November 2016.
- M. DeVos, J. McDonald and I. Pivotto (2016) Packing Steiner Trees. Journal of Combinatorial Theory Series B 119: 178-213. [arXiv] [Journal]
- J. Asplund and J. McDonald (2016) On a limit of the method of Tashkinov trees for edge-colouring, Discrete Math. 339(9): 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 (2015) Minimum (n,k,t) clique graphs. Congressus Numerantium 223: 199-204.
- M. DeVos, Z. Dvorak, J. Fox, J. McDonald, B. Mohar and D. Scheide (2014) A minimum degree condition forcing complete graph immersion. Combinatorica 34(3): 279-298. [arXiv] [Journal]
- G. Chapuy, M. DeVos, J. McDonald, B. Mohar and D. Scheide (2014) Packing triangles in weighted graphs. SIAM Journal on Discrete Mathematics 28(1): 226-239. [Journal]
- P. Johnson and J. McDonald (2013) Note on the inverse domination number problem. Congressus Numerantium 215: 47-51.
- M. DeVos, J. McDonald, B. Mohar, and D. Scheide (2013) A note on forbidding clique immersions. Electronic Journal of Combinatorics 20(3): #P55 (5 pages). [Journal]
- M. DeVos, J. McDonald, and D. Scheide (2013) Average degree in graph powers. Journal of Graph Theory 72(1): 7-18. [arXiv] [Journal]
- M. DeVos, J. McDonald, B. Mohar and D. Scheide (2012) Immersing complete digraphs. European Journal of Combinatorics 33(6): 1294-1302. [arXiv] [Journal]
- J. McDonald, B. Mohar, D. Scheide (2012) Kempe equivalence of edge-colourings in subcubic and subquartic graphs. Journal of Graph Theory 70(2): 226-239. [arXiv] [Journal]
- P. Haxell and J. McDonald (2012) On Characterizing Vizing's Edge-Colouring Bound. Journal of Graph Theory 69(2): 160-168. [Journal]
- J. M. McDonald (2011) On a Theorem of Goldberg. Journal of Graph Theory 68(1): 8-21. [Journal]
- J. M. McDonald (2010) On multiples of simple graphs and Vizing's Theorem. Discrete Mathematics 310(15-16): 2212-2214. [Journal]
- J. M. McDonald (2009) Achieving maximum chromatic index in multigraphs. Discrete Mathematics 309(8): 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]