6 citations · 34 across the 27 of their papers we have counts for
7 papers · 1 filter
The Zarankiewicz problem on tripartite graphs
Francesco Di Braccio, Freddie Illingworth
In 1975, Bollobás, Erdős, and Szemerédi asked for the smallest such that an tripartite graph with minimum degree must contain , conje…
Exponential odd-distance sets under the Manhattan metric
Alberto Espuny Díaz, Emma Hogan, Freddie Illingworth +3
We construct a set of points in such that all pairwise Manhattan distances are odd integers, which improves the recent linear lower bound of Golovanov, Kupavsk…
Spanning spheres in Dirac hypergraphs
Freddie Illingworth, Richard Lang, Alp Müyesser +2
We show that a -uniform hypergraph on vertices has a spanning subgraph homeomorphic to the -dimensional sphere provided that has no isolated vertices and each s…
When -intersecting hypergraphs admit bounded -strong colourings
Kevin Hendrey, Freddie Illingworth, Nina Kamčev +1
The -strong chromatic number of a hypergraph is the smallest number of colours needed to colour its vertices so that every edge sees at least colours or is rainbow. We show…
Dominating -Models
Freddie Illingworth, David R. Wood
A $\textit{dominating $K_t$-model}$ in a graph is a sequence of pairwise disjoint non-empty connected subgraphs of , such that for $1 \leqslant i<j \leqsla…
Fat minors cannot be thinned (by quasi-isometries)
James Davies, Robert Hickingbotham, Freddie Illingworth +1
We disprove the conjecture of Georgakopoulos and Papasoglu that a length space (or graph) with no -fat minor is quasi-isometric to a graph with no minor. Our counterexam…
Non-Homotopic Drawings of Multigraphs
António Girão, Freddie Illingworth, Alex Scott +1
A multigraph drawn in the plane is non-homotopic if no two edges connecting the same pair of vertices can be continuously deformed into each other without passing through a vertex,…