Our proof that every drawing of the complete graph in the plane must have at least 219 crossings is summarized on arxiv here. It is joint work with S. Pan and R. B. Richter. An improved version has since appeared and is available in JCT-B; the link to the improved version is here. In fact this new version was declared to be JCT-B’s “Hottest paper” for 6 months, starting in July 2015.
This preprint, Witt cancellation seen as a cancellation, is on the Witt Cancellation Theorem, with extra information about the Witt Ring. It is joint work with Sunil Chebolu and Ján Mináč. The illustrations are by Matthew Teigen.
Here are the slides for my talk, “Vertex-magic graphs,” from June 11, 2011, at the spring meeting of the Northeastern Section of the Mathematical Association of America.
While Katy Smith and I have a very elegant result on vertex-magic total labelings of odd complete graphs (link here), we also have a smaller paper with a similar sounding title, but on a different topic, with a much different result, on multiple complete graphs. Here is a preparing of this lesser known paper, Vertex magic total labelings of multiple complete graphs.
Another much older paper on vertex magic total labeling of cubic graphs, was a “major conceptual step forward,” according to the introduction of this paper. A preprint of the cubic graphs paper can be found here.