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- Darren B. Parker
- 2005

The results of this thesis are motivated by problems in the descent theory of coalgebras and Hopf algebras. If H and H ′ are coalgebras (or Hopf algebras) over the same field K, we attempt to find… (More)

- Darren B. Parker, Randy F. Westhoff, Marty J. Wolf
- Eur. J. Comb.
- 2008

In the context of two-path convexity, we study the rank, Helly number, Radon number, Caratheodory number, and hull number for multipartite tournaments. We show the maximum Caratheodory number of a… (More)

- Darren B. Parker, Randy F. Westhoff, Marty J. Wolf
- Australasian J. Combinatorics
- 2006

We present some results on two-path convexity in clone-free regular multipartite tournaments. After proving a structural result for regular multipartite tournaments with convexly independent sets of… (More)

- Darren B. Parker, Randy F. Westhoff, Marty J. Wolf
- Discussiones Mathematicae Graph Theory
- 2009

We investigate the convex invariants associated with two-path convexity in clone-free multipartite tournaments. Specically , we explore the relationship between the Helly number, Radon number and… (More)

We study two-path convexity in bipartite tournaments. For a bipartite tournament, we obtain both a necessary condition and a sufficient condition on the adjacency matrix for its rank to be two. We… (More)

- Atif A. Abueida, Wiebke S. Diestelkamp, Stephanie P. Edwards, Darren B. Parker
- Australasian J. Combinatorics
- 2005

The collection of convex subsets of a multipartite tournament T forms a lattice C(T). Given a lattice structure for C(T), we deduce properties of T. In particular, we flnd conditions under which we… (More)

The Lights Out game on a graph G is played as follows. Begin with a (not necessarily proper) coloring of V (G) with elements of Z2. When a vertex is toggled, that vertex and all adjacent vertices… (More)

- Darren B. Parker
- Ars Comb.
- 2018

- Darren B. Parker, Randy F. Westhoff
- Australasian J. Combinatorics
- 2012

In the study of convexity spaces, the most common convex invariants are based on notions of independence with respect to taking convex hulls. In [D.B. Parker, R.F. Westhoff and M.J. Wolf, Discuss.… (More)

- Darren B. Parker
- 2001

This paper studies the structure of U(g)-Galois extensions. In particular, we use a result of Bell to construct a “PBW-like” free basis for faithfully flat U(g)-Galois extensions. We then move to… (More)