Daniel Horsley

activity

20242026

collaborators

6 papers

math.CO2026

Determining decomposition thresholds for long odd cycles

Bertille Granet, Daniel Horsley

An $ℓ$ -cycle decomposition of a graph $G$ is a set of $ℓ$ -cycles in $G$ whose edge sets partition the edge set of $G$ . The $ℓ$ -cycle decomposition threshold $I^´_{C_{ℓ}}$ …

math.CO2026

On decomposition thresholds for odd-length cycles and other tripartite graphs

Darryn Bryant, Peter Dukes, Daniel Horsley +2

An (edge) decomposition of a graph $G$ is a set of subgraphs of $G$ whose edge sets partition the edge set of $G$ . Here we show, for each odd $ℓ \geq 5$ , that any graph $G$ of s…

math.CO2025

Completing partial $k$ -star designs

Ajani De Vas Gunasekara, Daniel Horsley

A $k$ -star is a complete bipartite graph $K_{1, k}$ . A partial $k$ -star design of order $n$ is a pair $(V, A)$ where $V$ is a set of $n$ vertices and $A$ is a set…

math.CO2025

Packing Designs with large block size

Andrea C. Burgess, Peter Danziger, Daniel Horsley +1

Given positive integers $v$ , $k$ , $t$ and $I^»$ with $v \geq k \geq t$ , a packing design PD $_{I^} » (v, k, t)$ is a pair $(V, B)$ , where $V$ is a $v$ -set and $B$ is a co…

math.CO2025

The semi-inducibility problem

Abdul Basit, Bertille Granet, Daniel Horsley +2

Let $H$ be a $k$ -edge-coloured graph and let $n$ be a positive integer. What is the maximum number of copies of $H$ in a $k$ -edge-coloured complete graph on $n$ vertices? This pape…

math.CO2024

Excess Coverage Arrays and Levenshtein's Conjecture

Amber E. Gentle, Daniel Horsley, Ian M. Wanless

A sequence covering array, denoted \textsf{SCA} $(N; t, v)$ , is a set of $N$ permutations of ${0, \dots, v - 1}$ such that each sequence of $t$ distinct elements of $\{0, \dots, v-1\…

Determining decomposition thresholds for long odd cycles

On decomposition thresholds for odd-length cycles and other tripartite graphs

Completing partial k-star designs

Packing Designs with large block size

The semi-inducibility problem

Excess Coverage Arrays and Levenshtein's Conjecture

Completing partial $k$ -star designs