Ph.D Advisor

• Professor D.S. Passman
  

Research

• Convexity, Graph Theory, Coalgebras, Hopf Algebras, and whatever else gets thrown my way.
• Description of my research interests.

Teaching Stuff

• My teaching philosophy.

More Professional Stuff

• My curriculum vitae.

Publications and Submissions.

• D.B. Parker, R.F. Westhoff, and M.J. Wolf, Convex Independence and the Structure of Clone-Free Multipartite Tournaments (submitted to Discussiones Mathematicae)
• D.B. Parker, R.F. Westhoff, and M.J. Wolf, Two-Path Convexity and Bipartite Tournaments of Small Rank, (to appear in Ars Combinatoria).
• D.B. Parker, R.F. Westhoff, and M.J. Wolf, On Two-Path Convexity in Multipartite Tournaments, European Journal of Combinatorics 29 (2008), pp. 641-651.
• A. Abueida, M. Daven, W.S. Diestelkamp, S.P. Edwards, and D.B. Parker, Multidesigns for Graph-Triples of Order 6, Congressus Numerantium 183 (2006), pp. 139-160.
• D.B. Parker, R.F. Westhoff, and M.J. Wolf, Two-Path Convexity in Clone-Free Regular Multipartite Tournaments, Australasian Journal of Combinatorics 36 (2006), pp. 177-196..
• A. Abueida, W.S. Diestelkamp, S.P. Edwards, and D.B. Parker, Determining Properties of a Multipartite Tournament from its Lattice of Convex Subsets, Australasian Journal of Combinatorics 31 (2005), pp. 217-230.
• D.B. Parker, On the Coradical Filtration of Pointed Coalgebras, Journal of Algebra 255 (2002), pp. 121-134.
• D.B. Parker, U(g)-Galois Extensions, Communications in Algebra 29 (2001), pp. 2859-2870.
• D.B. Parker, Forms of Coalgebras and Hopf Algebras, Journal of Algebra 239 (2001), pp. 1-34.
• D.B. Parker, Hopf Galois Extensions and Forms of Coalgebras and Hopf Algebras, Doctoral Thesis.

Works in Progress.

• A. Giffen and D.B. Parker, An Examination of the Lights Out Game on Paths, Cycles, and Caterpillars, (in progress).
• D.B. Parker, R.F. Westhoff, and M.J. Wolf, Cycles in Bipartite Tournaments of Rank 2, (in progress).
• D.B. Parker, R.F. Westhoff, and M.J. Wolf, Convex Invariants in Multipartite Tournaments, (in progress).

Current Projects.

• With R.F. Westhoff and M.J. Wolf: We are studying multipartite tournaments and their convex subsets under two-path convexity. In particular, we are studying a convexity invariant called rank. Rank is an upper bound for the Helly number, the Caratheodory number, and the Radon number, the three most central numbers in abstract convexity theory. In addition, it is an upper bound for the hull number, as well as the number of vertices required to generate all convex subsets using convex hulls. In particular, we are interested in finding classes of digraphs for which the Helly number, Radon number, and rank are all equal.

• With A. Abueida, W. Diestelkamp, and S. Edwards: We are studying multidesigns. We seek to decompose the edges of K_n using three non-isomorphic graphs that factor K_6 without isolated vertices. We are looking into which K_n admit decompositions of such triples.

• With B. Duncan and S. Edwards: We are working on an algorithm for a targeting system using prisms and lasers. A little engineering to shake us up.

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