I am a graph theorist, broadly interested in structure and colouring, among other things.
- J. McDonald. A list analog of Vizing's Theorem for simple graphs with triangles but no other odd cycles, submitted. [arXiv]
- M. DeVos, J. McDonald and I. Pivotto. Packing Steiner Trees, submitted. [arXiv]
- J. McDonald. Edge-colourings, in: Topics in Chromatic Graph Theory (eds. L. W. Beineke and R. J. Wilson), Cambridge University Press, to appear.
- L. Anderson, M. DeVilbiss, S. Holliday, P. Johnson, A. Kite, R. Matzke and J. McDonald. The edge Grundy numbers of some graphs, submitted.
- 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]
- In Fall 2014 I am teaching Math 5750/6750 (Graph Theory) and Math 3710/ Comp 3240 (Discrete Math/Discrete Structures).
- In Spring 2014 I taught Math 3710/ Comp 3240 (Discrete Math/ Discrete Structures).
- In Fall 2013 I taught Math 6750 (Graph Theory) and Math 5710/6710 (Linear Optimization).
- In Spring 2013 I taught Math 7750/7970 (Advanced Graph Theory) and Math 3710/ Comp 3240 (Discrete Math/ Discrete Structures).
- In Fall 2012 I taught Math 5750 (Graph Theory).
Before coming to Auburn I was an NSERC Postdoctoral Fellow in the Department of Mathematics at Simon Fraser University, sponsored by Bojan Mohar. Prior to that I was at IPAM at UCLA, as part of a special semester in Combinatorics. My PhD (2009) is from the Department of Combinatorics and Optimization at the University of Waterloo, and my advisor was Penny Haxell. I also have an M. Math degree from the C&O Department at Waterloo (supervised by D.H. Younger), and an undergraduate degree in math (BScH) from Mount Allison University.