Research

I am a graph theorist. I work on multigraph edge-colouring, immersion in graphs and digraphs, packing Steiner trees, Kempe equivalence of edge-colourings, graph powers, and Tuza's Conjecture on packing and covering triangles, among other things. Many of my papers have a preprint version available on the arXiv that I've linked to below; for my papers that have appeared I've also included a link to the final journal version.

• M. DeVos, J. McDonald and I. Pivotto. Packing Steiner Trees, in preparation.
• M. DeVos, J. McDonald, B. Mohar, and D. Scheide. A note on forbidding clique immersions, submitted. [arXiv]
• Z. Devorak, J. Fox, M. Devos, J. McDonald, B. Mohar and D. Scheide. Minimum degree forcing complete graph immersion, submitted. [arXiv]
• G. Chapuy, M. DeVos, J. McDonald, B. Mohar and D. Scheide. Packing triangles in weighted graphs, submitted. [arXiv]
• M. Devos, J. McDonald, and D. Scheide. Average degree in graph powers, accepted by Journal of Graph Theory. [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]

Teaching

In Fall 2012 I am teaching Math 5750 (Graph Theory).

Background

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.