My research is in graph theory and combinatorics. Lately I've been working on embedding problems for directed triple systems. Also, there is the question of establishing Hall-like conditions equivalent to the results in [1]. The results from [6] should be extended soon as well. Recently, the embedding problem for Stiener Triple systems has been solved and Lindner's Conjecture (1975) has proven to be true--as everyone expected. This brilliant paper by Bryant and Horsely will appear soon. I hope to establish a generalized amalgamation result for Steiner triple systems from this paper.
Papers:
1. with H. L. Buchanan II, "On completing Latin squares," J. Combinatorial Math. and Combinatorial Comp., 34 (2000), pp. 129--132.
2. with A. J. W. Hilton, "Pseudo-outline transitive triple systems," Proceedings of the 32nd Southeastern International Conference on Combinatorics, Graph Theory and Computing, Congr. Numer. 153 (2001), pp. 141--149. (Viewable .pdf)
3. with A. J. W. Hilton, "Outline and amalgamated triple systems of even index," Proc. London Math Soc. (3), 84 (2002), pp: 1--34. (Postscript preprint) (Viewable .pdf version)
4. with A. J. W. Hilton, "Outline and amalgamated transitive triple systems in the special case when just two veritces are amalgamated," Congr. Numer. 167 (2004), pp. 221--237. (Viewable .pdf)
5. with S. J. Curran, J. W. Thompson and S. Wieczorek, "Mathematically Speaking: Expanding the Role of Oral Communication in Mathematics," FOCUS (9) 25 (2005), pp. 12--13. (available at ww.maa.org)
6. with S. J. Curran, C. J. Morgan and J. W. Thompson, "The hamiltonicity of a Caley digraph of a modified abelian group on two generators," Congr. Numer. 188 (2007), pp. 75--95 . (Viewable .pdf)
7. with A. J. W. Hilton, "On (r,r+1)-factorizations of (d,d+1)-graphs", (in preparation).