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A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n=p 2 for an odd prime p. We construct a family of (p − 1)/2 non-isomorphic perfect 1-factorisations of K n, n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamilto-nian if the permutation defined by any… (More)

MOTIVATION
A consensus sequence for a family of related sequences is, as the name suggests, a sequence that captures the features common to most members of the family. Consensus sequences are important in various DNA sequencing applications and are a convenient way to characterize a family of molecules.
RESULTS
This paper describes a new algorithm for… (More)

Let H be a graph. A graph G is said to be H-free if it contains no subgraph isomorphic to H. A graph G is said to be an H-saturated subgraph of a graph K if G is an H-free subgraph of K with the property that for any edge e ∈ E(K) \ E(G); G ∪ {e} is not H-free. We present some general results on Ks;t-saturated subgraphs of the complete bipartite graph Km;n… (More)

Cyclic m-cycle systems of order v are constructed for all m ≥ 3, and all v ≡ 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for… (More)

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n 2 − k cells diierent in all three latin squares, denoted by I 3 [n], is determined here for all orders n.

Despite the success of conventional Sanger sequencing, significant regions of many genomes still present major obstacles to sequencing. Here we propose a novel approach with the potential to alleviate a wide range of sequencing difficulties. The technique involves extracting target DNA sequence from variants generated by introduction of random mutations.… (More)