Thomas Lesgourgues

activity

20202026

most citedThe minimum degree of minimal Ramsey graphs for cliques

3 citations · 3 across the 9 of their papers we have counts for

collaborators

13 papers

math.CO2026

Improved bounds on completion of partial Latin squares

Jack Allsop, Candida Bowtell, Thomas Lesgourgues +1

A Latin square of order $n$ is an $n \times n$ array filled with $n$ symbols so that each symbol appears exactly once in every row and column. A partial Latin square of order $n$ i…

math.CO2026

A Combinatorial Proof of Hilton's Conjecture and Beyond

Thomas Lesgourgues, Luke Postle

Using refined absorption, we prove that for every integer $g \geq 1$ and real $γ > 0$ , and for sufficiently large $n$ , there exists an $n^{- 1 + γ}$ -spread distribution on Latin squares…

math.CO2025

Odd-Ramsey numbers of Hamilton cycles

Simona Boyadzhiyska, Shagnik Das, Thomas Lesgourgues +1

The odd-Ramsey number $r_{o dd} (n, H)$ of a graph $H$ , as introduced by Alon in his work on graph-codes, is the minimum number of colours needed to edge-colour $K_{n}$ so that ev…

math.CO2025

Fractional Clique Decompositions of Dense Hypergraphs

Michelle Delcourt, Thomas Lesgourgues, Luke Postle

In 2014, Keevash famously proved the existence of $(n, q, r)$ -Steiner systems as part of settling the Existence Conjecture of Combinatorial Designs (dating from the mid-1800s). In 20…

math.CO2025

Beyond Nash-Williams: Counterexamples to Clique Decomposition Thresholds for All Cliques Larger than Triangles

Michelle Delcourt, Cicely Henderson, Thomas Lesgourgues +1

A central open question in extremal design theory is Nash-Williams' Conjecture from 1970 that every $K_{3}$ -divisible graph on $n$ vertices (for $n$ large enough) with minimum degree…

math.CO2025

Erdős meets Nash-Williams

Michelle Delcourt, Cicely, Henderson +2

In 1847, Kirkman proved that there exists a Steiner triple system on $n$ vertices (equivalently a triangle decomposition of the edges of $K_{n}$ ) whenever $n$ satisfies the necessary…

math.CO2025

Ramsey with purple edges

Thomas Lesgourgues, Anita Liebenau, Nye Taylor

Motivated by a question of Angell, we investigate a variant of Ramsey numbers where some edges are coloured simultaneously red and blue, which we call purple. Specifically, we are…

math.CO2024

Odd-Ramsey numbers of complete bipartite graphs

Simona Boyadzhiyska, Shagnik Das, Thomas Lesgourgues +1

In his study of graph codes, Alon introduced the concept of the odd-Ramsey number of a family of graphs $H$ in $K_{n}$ , defined as the minimum number of colours needed to c…

math.CO2024

Clustered Colouring of Graph Products

Rutger Campbell, J. Pascal Gollin, Kevin Hendrey +5

A colouring of a graph $G$ has clustering $k$ if the maximum number of vertices in a monochromatic component equals $k$ . Motivated by recent results showing that many natural graph…

math.CO2022

On the use of senders for asymmetric tuples of cliques in Ramsey theory

Simona Boyadzhiyska, Thomas Lesgourgues

A graph $G$ is $q$ -Ramsey for a $q$ -tuple of graphs $(H_{1}, \dots, H_{q})$ if for every $q$ -coloring of the edges of $G$ there exists a monochromatic copy of $H_{i}$ in color $i$ for som…

math.CO2022

A new upper bound on the minimum degree of minimal Ramsey graphs

Anurag Bishnoi, Thomas Lesgourgues

We prove that $s_{r} (K_{k + 1}) = O (k^{3} r^{3} lo g^{3} k)$ , where $s_{r} (K_{k})$ is the Ramsey parameter introduced by Burr, Erdős and Lovász in 1976, which is defined as the smallest minimum…

math.CO2021

On the minimum degree of minimal Ramsey graphs for cliques versus cycles

Anurag Bishnoi, Simona Boyadzhiyska, Dennis Clemens +3

A graph $G$ is said to be $q$ -Ramsey for a $q$ -tuple of graphs $(H_{1}, \dots, H_{q})$ , denoted by $G \to_{q} (H_{1}, \dots, H_{q})$ , if every $q$ -edge-coloring of $G$ contains a monochromatic c…

math.CO2020★ 3 cited

The minimum degree of minimal Ramsey graphs for cliques

John Bamberg, Anurag Bishnoi, Thomas Lesgourgues

We prove that $s_{r} (K_{k}) = O (k^{5} r^{5/2})$ , where $s_{r} (K_{k})$ is the Ramsey parameter introduced by Burr, Erdős and Lovász in 1976, which is defined as the smallest minimum degree of…