Lukas Michel

collaborators

4 papers

math.CO2023

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…

math.CO2023

Circuit decompositions of binary matroids

Bryce Frederickson, Lukas Michel

Given a simple Eulerian binary matroid $M$ , what is the minimum number of disjoint circuits necessary to decompose $M$ ? We prove that $∣ M ∣/ (rank (M) + 1)$ many circ…

math.CO2023

Flashes and rainbows in tournaments

António Girão, Freddie Illingworth, Lukas Michel +2

Colour the edges of the complete graph with vertex set ${1, 2, \dots, n}$ with an arbitrary number of colours. What is the smallest integer $f (l, k)$ such that if $n > f (l, k)$ th…

math.CO2023

Reconstructing a point set from a random subset of its pairwise distances

António Girão, Freddie Illingworth, Lukas Michel +2

Let $V$ be a set of $n$ points on the real line. Suppose that each pairwise distance is known independently with probability $p$ . How much of $V$ can be reconstructed up to isometr…