Deciding whether an arbitrary partial commutative quasigroup can be completed is known to be NP-complete. Here, we prove that it remains NP-complete even if the partial quasigroup is constructed, in...
Computing the distribution of a tree metric (2009)
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an...
Counting ancestral reconstructions in a fixed phylogeny (2008)
Tobias Thierer A, David Bryant B, Mike Steel D, T. Thierer, D. Bryant, M. Steel
We give formulas for calculating in polynomial time the number of ancestral reconstructions for a tree with binary leaf- and root labels for each number of 0 → 1 and 1 → 0 arcs. For trees of...
Completing partial Latin squares with two filled rows and two filled columns (2008)
Adams, P., Bryant, D., Buchanan, M.
It is shown that any partial Latin square of order at least six which consists of two lled rows and two lled columns can be completed.
Counting Ancestral Reconstructions in a Fixed Phylogeny (2008)
Thierer, T., Bryant, D., Steel, M.
We give formulas for calculating in polynomial time the number of ancestral reconstructions for a tree with binary leaf- and root labels for each number of 0 → 1 and 1 → 0 arcs. For trees of...
The use of fluorescent probes for the detection of under-film corrosion (2006)
An inexpensive and practical method for detecting under-film aluminium corrosion using a hand-held UV inspection lamp is described. A novel fluorescent probe for under-film iron corrosion is...
On the completion of Latin rectangles to symmetric Latin squares (2004)
We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n...
Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves (2004)
Bryant, D., Maenhaut, B., Quinn, K., Webb, B. S.
Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the...
On the volume of 4-cycle trades (2003)
Bryant, D., Grannell, M., Griggs, T., Maenhaut, B.
A 4-cycle trade of volume t corresponds to a simple graph G without isolated vertices, where the edge set can be partitioned into t 4-cycles in at least two different ways such that the two...
Skolem-type difference sets for cycle systems (2003)
Bryant, D., Gavlas, H., Ling, A. C. H.
Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a...
Large sets of large sets of Steiner triple systems of order 9 (2003)
Bryant, D., Grannell, M., Griggs, T.
We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply...
The size of a maximum agreement subtree for random binary trees (2003)
Bryant, D., McKenzie, A., Steel, M.
First published in BioConsensus, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 61, pp. 55-65., published by the American Mathematical Society