**Since 2009**

Alan Arroyo, Dan McQuillan, R. Bruce Richter and Gelasio Salazar, Levi’s Lemma, pseudolinear drawings of K_n and empty triangles, Journal of Graph Theory, to appear in 2018. Available online here.

Dan McQuillan and James M. McQuillan, Strong vertex-magic and edge-magic labelings of 2-regular graphs of odd order using Kotzig completion, Discrete Mathematics, Volume 341, Issue 1, January 2018, pp. 194-202. Available here.

Sunil K. Chebolu, Dan McQuillan and Jan Minac, Witt’s Cancellation Theorem seen as a cancellation, Expositiones Mathematicae, September 2017. Available online here.

Alan Arroyo, Dan McQuillan, R. Bruce Richter and Gelasio Salazar, Drawings of K_n with the same rotation scheme are the same up to triangle-flips (Gioan’s Theorem), Australasian Journal of Combinatorics, Volume 67, Issue 2, February 2017, pp. 131-144. Available online here.

Dan McQuillan and R. Bruce Richter, On the crossing number of K_n without computer assistance, Journal of Graph Theory, Volume 82, Issue 4, August 2016, pp. 387-432. Available online here.

Dan McQuillan and Darlene Olsen, A truly beautiful theorem: demonstrating the magnificence of the fundamental theorem of calculus, Journal of Humanistic Mathematics, Volume 6, Issue 2, July 2016, pp. 148-160. The full paper is available here.

Skylar Croy, Jeremy Hansen and Dan McQuillan, Calculating the number of order-6 magic squares with modular lifting, (2 page extended abstract) Proceedings of the Ninth Annual Symposium on Combinatorial Search, (SoCS 2016) July 2016, pp. 129-130. Available online here.

Peter MacDonald, Dan McQuillan and Ian McQuillan, Run for Third! A Defense of Aggressive Base Running, Math Horizons, Volume 23, Issue 4, April 2016, pp. 14-15.

Dan McQuillan, Shengjun Pan and R. Bruce Richter, On the crossing number of K_13, Journal of Combinatorial Theory, Series B, Volume 115, November 2015, pp. 224-235.

Dan McQuillan and Rob Poodiack, On the differentiation formuale for sine, tangent and inverse tangent, College Mathematics Journal, Vol. 45, No. 2, (2014), pp. 140-142.

James M. McQuillan and Dan McQuillan, Algorithms for finding magic labelings of triangles, The 2012 International Conference of Foundations of Computer Science, FCS 2012, Hamid R. Arabnia, George A. Gravvanis and Ashu M.G. Solo eds., CSREA Press, Las Vegas, Nevada, July 2012, pp. 3-8. (refereed conference proceeding, acceptance rate 29%).

Addie Armstrong and Dan McQuillan, Vertex-magic total labelings of even complete graphs, Discrete Math. 311 (2011) pp. 676-683.

Dan McQuillan, A technique for constructing magic labelings of 2-regular graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 75 (2010), pp. 129-135.

Dan McQuillan and R. Bruce Richter, A Parity Theorem for Drawings of Complete and Complete Bipartite Graphs, American Mathematical Monthly Vol. 117, No. 3, March 2010.

Jeremy Holden, Dan McQuillan and James M. McQuillan, A conjecture on strong magic labelings of 2-regular graphs, Discrete Mathematics, 309 (2009), pp. 4130-4136.

Dan McQuillan and James M. McQuillan, Magic Labelings of Triangles, Discrete Mathematics, 309 (2009), pp. 2755-2762.

Dan McQuillan, Edge-magic and Vertex magic Total Labelings of Certain Cycles, Ars Combinatoria, 91(2009), pp. 257-266.

**With students**

Here are some of the highlights from work done with excellent mathematicians (Katy Smith, Jeremy Holden, Addie Armstrong and Skylar Croy) who were undergraduate students at the time that the main part of the work for these papers was done.

Skylar Croy, Jeremy Hansen and Dan McQuillan, Calculating the number of order-6 magic squares with modular lifting, (2 page extended abstract) Proceedings of the Ninth Annual Symposium on Combinatorial Search, (SoCS 2016) July 2016, pp. 129-130. Available online here.

Addie Armstrong and Dan McQuillan, Vertex-magic total labelings of even complete graphs, Discrete Math. 311 (2011) pp. 676-683.

Jeremy Holden, Dan McQuillan and James M. McQuillan, A conjecture on strong magic labelings of 2-regular graphs, Discrete Mathematics, 309 (2009), pp. 4130-4136.

Dan McQuillan and Katy Smith, Vertex-magic total labeling of multiple complete graphs, Congressus Numerantium 180 (2006) pp. 201-205.

Dan McQuillan and Katy Smith, Vertex-magic total labeling of odd complete graphs, Discrete Math. 305 (2005) pp. 240-249.