Daniel Horsley

activity

20122022

most citedDecompositions of complete graphs into cycles of arbitrary lengths

54 citations · 108 across the 24 of their papers we have counts for

collaborators

Showing 2014 · math.COShow all

5 papers · 2 filters

math.CO2014

On factorisations of complete graphs into circulant graphs and the Oberwolfach Problem

Brian Alspach, Darryn Bryant, Daniel Horsley +2

Various results on factorisations of complete graphs into circulant graphs and on 2-factorisations of these circulant graphs are proved. As a consequence, a number of new results o…

math.CO2014

Doyen-Wilson results for odd length cycle systems

Daniel Horsley, Rosalind A. Hoyte

For each odd $m \geq 3$ we completely solve the problem of when an $m$ -cycle system of order $u$ can be embedded in an $m$ -cycle system of order $v$ , barring a finite number of pos…

math.CO2014

Generalising Fisher's inequality to coverings and packings

Daniel Horsley

In 1940 Fisher famously showed that if there exists a non-trivial $(v, k, λ)$ -design then $λ (v - 1) \geq k (k - 1)$ . Subsequently Bose gave an elegant alternative proof of Fisher's result…

math.CO2014

Steiner triple systems without parallel classes

Darryn Bryant, Daniel Horsley

We construct Steiner triple systems without parallel classes for an infinite number of orders congruent to $3 (mod 6)$ . The only previously known examples have order $15$ or $21$ .

math.CO2014

Embedding partial Steiner triple systems with few triples

Daniel Horsley

It was proved in 2009 that any partial Steiner triple system of order $u$ has an embedding of order $v$ for each admissible integer $v \geq 2 u + 1$ . This result is best-possible in th…