Daniel Horsley

activity

20232026

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Showing 2024Show all

5 papers · 1 filter

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\…

math.CO2024

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.CO2024

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.CO2024

Packing Designs with large block size

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

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

math.CO2024

Completing the solution of the directed Oberwolfach problem with two tables

Daniel Horsley, Alice Lacaze-Masmonteil

We address the last outstanding case of the directed Oberwolfach problem with two tables of different lengths. Specifically, we show that the complete symmetric directed graph $K^*…

Excess Coverage Arrays and Levenshtein's Conjecture

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

Completing partial k-star designs

Packing Designs with large block size

Completing the solution of the directed Oberwolfach problem with two tables

Completing partial $k$ -star designs