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…
Circuit decompositions of binary matroids
Bryce Frederickson, Lukas Michel
Given a simple Eulerian binary matroid , what is the minimum number of disjoint circuits necessary to decompose ? We prove that many circ…
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…
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…