1 citations · 1 across the 7 of their papers we have counts for
8 papers · 1 filter
The regular pentagon is canonically Ramsey
Benedict Randall Shaw
A set of points is canonically Ramsey if there is some larger set of points such that any colouring of contains either a mono…
Products of simplices are canonically Ramsey
Benedict Randall Shaw
A set of points is called canonically Ramsey if there is some set of points such that any colouring of , using any number of…
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…
Connecting hypercube 1-factors
Lawrence Hollom, Benedict Randall Shaw
A 1-factorisation of a regular graph is a partition of its edge set into perfect matchings of . Behague asked for the minimal such that some -factorisatio…
Minimal hypergraph non-jumps
Benedict Randall Shaw
An -uniform hypergraph, or -graph, has density . We say is a jump for -graphs if there is some constant such that, for each $\varepsilon>…
New optima for the deletion shadow
Benedict Randall Shaw
For a family of words of length drawn from an alphabet , Danh and Daykin defined the deletion shadow as the family containing…
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…
Reconstructing almost all of a point set in from randomly revealed pairwise distances
Douglas Barnes, Jan Petr, Julien Portier +2
Let be a set of points in , and suppose that the distance between each pair of points is revealed independently with probability . We study when this infor…