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

collaborators

9 papers

math.CO2026

The regular pentagon is canonically Ramsey

Benedict Randall Shaw

A set of points $C \subset R^{n}$ is canonically Ramsey if there is some larger set of points $S \subset R^{n^{'}}$ such that any colouring of $S$ contains either a mono…

math.CO2026

Products of simplices are canonically Ramsey

Benedict Randall Shaw

A set of points $C \subset R^{n}$ is called canonically Ramsey if there is some set of points $S \subset R^{n^{'}}$ such that any colouring of $S$ , using any number of…

cs.CY2026

CrisiSense-RAG: Crisis Sensing Multimodal Retrieval-Augmented Generation for Rapid Disaster Impact Assessment

Yiming Xiao, Kai Yin, Ali Mostafavi

Timely and spatially resolved disaster impact assessment is essential for effective emergency response. However, automated methods typically struggle with temporal asynchrony. Real…

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…

math.CO2024★ 1 cited

Completely independent spanning trees in the hypercube

Benedict Randall Shaw

We say two spanning trees of a graph are completely independent if their edge sets are disjoint, and for each pair of vertices, the paths between them in each spanning tree do not…

math.CO2024

Reconstructing almost all of a point set in $R^{d}$ from randomly revealed pairwise distances

Douglas Barnes, Jan Petr, Julien Portier +2

Let $V$ be a set of $n$ points in $R^{d}$ , and suppose that the distance between each pair of points is revealed independently with probability $p$ . We study when this infor…

The regular pentagon is canonically Ramsey

Products of simplices are canonically Ramsey

CrisiSense-RAG: Crisis Sensing Multimodal Retrieval-Augmented Generation for Rapid Disaster Impact Assessment

Counterexamples to conjectures on strong maximality and minimality

Connecting hypercube 1-factors

Minimal hypergraph non-jumps

New optima for the deletion shadow

Completely independent spanning trees in the hypercube

Reconstructing almost all of a point set in Rd from randomly revealed pairwise distances

Reconstructing almost all of a point set in $R^{d}$ from randomly revealed pairwise distances