L. Michel

activity

20232025

collaborators

10 papers

math.CO2025

Cycle-factors of regular graphs via entropy

Micha Christoph, Nemanja Draganić, António Girão +3

It is a classical result that a random permutation of $n$ elements has, on average, about $lo g n$ cycles. We generalise this fact to all directed $d$ -regular graphs on $n$ vertice…

math.CO2025

New bounds for linear arboricity and related problems

Micha Christoph, Nemanja Draganić, António Girão +3

A linear forest is a collection of vertex-disjoint paths. The Linear Arboricity Conjecture states that every graph of maximum degree $Δ$ can be decomposed into at most $\lceil(Δ+1)…

math.CO2024

Exponential odd-distance sets under the Manhattan metric

Alberto Espuny Díaz, Emma Hogan, Freddie Illingworth +3

We construct a set of $2^{n}$ points in $R^{n}$ such that all pairwise Manhattan distances are odd integers, which improves the recent linear lower bound of Golovanov, Kupavsk…

math.CO2024

Small families of partially shattering permutations

António Girão, Lukas Michel, Youri Tamitegama

We say that a family of permutations $t$ -shatters a set if it induces at least $t$ distinct permutations on that set. What is the minimum number $f_{k} (n, t)$ of permutations of $\{1,…

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

Chromatic number is not tournament-local

António Girão, Kevin Hendrey, Freddie Illingworth +4

Scott and Seymour conjectured the existence of a function $f : N \to N$ such that, for every graph $G$ and tournament $T$ on the same vertex set, $χ(G) \geqs…

math.CO2023

The structure and density of $k$ -product-free sets in the free semigroup

Freddie Illingworth, Lukas Michel, Alex Scott

The free semigroup $F$ over a finite alphabet $A$ is the set of all finite words with letters from $A$ equipped with the operation of concatenation. A…

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…

Cycle-factors of regular graphs via entropy

New bounds for linear arboricity and related problems

Exponential odd-distance sets under the Manhattan metric

Small families of partially shattering permutations

Abundance: Asymmetric Graph Removal Lemmas and Integer Solutions to Linear Equations

Circuit decompositions of binary matroids

Flashes and rainbows in tournaments

Chromatic number is not tournament-local

The structure and density of k-product-free sets in the free semigroup

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

The structure and density of $k$ -product-free sets in the free semigroup