6 citations · 34 across the 27 of their papers we have counts for
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Asymptotic dimension of graphs excluding an induced or fat minor
Robert Hickingbotham, Freddie Illingworth, Piotr Micek +1
Asymptotic dimension is a large-scale invariant of metric spaces that was introduced by Gromov (1993). A major open problem in coarse graph theory asks whether, for every fixed gra…
Hypergraphs with the smallest Hall ratio are still hard to colour
Veronica Bitonti, Freddie Illingworth, Pedram Noohi +1
For a hypergraph, the Hall ratio is a natural lower bound for its chromatic number, and among non-empty -u…
Disproof of the dominating Hadwiger conjecture
Freddie Illingworth, Raphael Steiner
Hadwiger's conjecture (1943) states that every graph with chromatic number at least contains a -model: a collection of vertex-disjoint connected subgraphs $T_1,\do…
Countable Graphs with Finite Path-width: Characterisation and Universality
Tony Huynh, Freddie Illingworth, Nikolai Karol +4
We study path-width and the closely related parameter line-width in countably infinite graphs. Our first result characterises the graphs of finite path-width: they are the graphs t…
Disproof of the tree product conjecture via the Heisenberg group
Freddie Illingworth, Sergey Norin, Raphael Steiner
Product structure theory aims to understand complex graphs by embedding them into products of simpler graphs. In this direction, Campbell, Distel, Gollin, Harvey, Hendrey, Hickingb…
The Dominating 4-Colour Theorem
António Girão, Freddie Illingworth, Bojan Mohar +6
A "dominating -model" in a graph is a sequence of pairwise vertex-disjoint connected subgraphs of , such that whenever every vertex…