Benedict Randall Shaw

activity

20242026

most citedCompletely independent spanning trees in the hypercube

1 citations · 1 across the 7 of their papers we have counts for

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4 papers · 1 filter

math.CO2025

Counterexamples to conjectures on strong maximality and minimality

Lawrence Hollom, Benedict Randall Shaw

We provide counterexamples to several conjectures concerning strongly maximal and strongly minimal structures in infinite graphs and hypergraphs. In particular, we construct 3-unif…

math.CO2025

Connecting hypercube 1-factors

Lawrence Hollom, Benedict Randall Shaw

A 1-factorisation of a regular graph $G$ is a partition of its edge set $E (G)$ into perfect matchings of $G$ . Behague asked for the minimal $r = r (d)$ such that some $1$ -factorisatio…

math.CO2025

Minimal hypergraph non-jumps

Benedict Randall Shaw

An $r$ -uniform hypergraph, or $r$ -graph, has density $∣ E (G) ∣/∣ V (G)^{(r)} ∣$ . We say $α$ is a jump for $r$ -graphs if there is some constant $δ = δ (α)$ such that, for each $\varepsilon>…

math.CO2025

New optima for the deletion shadow

Benedict Randall Shaw

For a family $F$ of words of length $n$ drawn from an alphabet $A = [r] = {1, \dots, r}$ , Danh and Daykin defined the deletion shadow $Δ F$ as the family containing…