6 citations · 34 across the 27 of their papers we have counts for
6 papers · 1 filter
Abundance: Asymmetric Graph Removal Lemmas and Integer Solutions to Linear Equations
António Girão, Eoin Hurley, Freddie Illingworth +1
We prove that a large family of pairs of graphs satisfy a polynomial dependence in asymmetric graph removal lemmas. In particular, we give an unexpected answer to a question of Gis…
Flashes and rainbows in tournaments
António Girão, Freddie Illingworth, Lukas Michel +2
Colour the edges of the complete graph with vertex set with an arbitrary number of colours. What is the smallest integer such that if th…
Chromatic number is not tournament-local
António Girão, Kevin Hendrey, Freddie Illingworth +4
Scott and Seymour conjectured the existence of a function such that, for every graph and tournament on the same vertex set, $χ(G) \geqs…
The structure and density of -product-free sets in the free semigroup
Freddie Illingworth, Lukas Michel, Alex Scott
The free semigroup over a finite alphabet is the set of all finite words with letters from equipped with the operation of concatenation. A…
On tree decompositions whose trees are minors
Pablo Blanco, Linda Cook, Meike Hatzel +3
In 2019, Dvořák asked whether every connected graph has a tree decomposition so that is a subgraph of and the width of is bounded…
Reconstructing a point set from a random subset of its pairwise distances
António Girão, Freddie Illingworth, Lukas Michel +2
Let be a set of points on the real line. Suppose that each pairwise distance is known independently with probability . How much of can be reconstructed up to isometr…