M. Delcourt

activity

20142026

most citedReducing Linear Hadwiger's Conjecture to Coloring Small Graphs

8 citations · 23 across the 20 of their papers we have counts for

collaborators

28 papers

math.CO2026

A Proof of Nash-Williams' Conjecture

Michelle Delcourt, Luke Postle

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

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.CO2024

A Short Proof of the Existence of $K_{q}^{r}$ -absorbers

Michelle Delcourt, Tom Kelly, Luke Postle

We codify a short self-contained proof of the existence of $K_{q}^{r}$ -absorbers implicit in Keevash's original proof of the Existence Conjecture. Combining this with the work of the f…

math.CO2024★ 1 cited

Sunflowers in set systems with small VC-dimension

József Balogh, Anton Bernshteyn, Michelle Delcourt +2

A family of $r$ distinct sets ${A_{1}, \dots, A_{r}}$ is an $r$ -sunflower if for all $1 ⩽ i < j ⩽ r$ and $1 ⩽ i^{'} < j^{'} ⩽ r$ , we have $A_i \cap A_j = A_…

math.CO2024

Thresholds for $(n, q, 2)$ -Steiner Systems via Refined Absorption

Michelle Delcourt, Tom Kelly, Luke Postle

We prove that if $p \geq n^{- (q - 6) /2}$ , then asymptotically almost surely the binomial random $q$ -uniform hypergraph $G^{(q)} (n, p)$ contains an $(n, q, 2)$ -Steiner system, provided $…

math.CO2024

Clique Decompositions in Random Graphs via Refined Absorption

Michelle Delcourt, Tom Kelly, Luke Postle

We prove that if $p \geq n^{- \frac{1}{3} + β}$ for some $β > 0$ , then asymptotically almost surely the binomial random graph $G (n, p)$ has a $K_{3}$ -packing containing all but at most $n +…

math.CO2024

Proof of the High Girth Existence Conjecture via Refined Absorption

Michelle Delcourt, Luke Postle

We prove the High Girth Existence Conjecture - the common generalization of the Existence Conjecture for Combinatorial Designs originating from the 1800s and Erdős' Conjecture from…

math.CO2024

Refined Absorption: A New Proof of the Existence Conjecture

Michelle Delcourt, Luke Postle

The study of combinatorial designs has a rich history spanning nearly two centuries. In a recent breakthrough, the notorious Existence Conjecture for Combinatorial Designs dating b…

math.CO2023

Decomposing random regular graphs into stars

Michelle Delcourt, Catherine Greenhill, Mikhail Isaev +2

We study $k$ -star decompositions, that is, partitions of the edge set into disjoint stars with $k$ edges, in the uniformly random $d$ -regular graph model $G_{n, d}$ . Using…

math.CO2022

On generalized Ramsey numbers in the non-integral regime

Patrick Bennett, Michelle Delcourt, Lina Li +1

A $(p, q)$ -coloring of a graph $G$ is an edge-coloring of $G$ such that every $p$ -clique receives at least $q$ colors. In 1975, Erdős and Shelah introduced the generalized Ramsey nu…

math.CO2022★ 1 cited

Almost all 9-regular graphs have a modulo-5 orientation

Michelle Delcourt, Reaz Huq, Pawel Pralat

In 1972 Tutte famously conjectured that every 4-edge-connected graph has a nowhere zero 3-flow; this is known to be equivalent to every 5-regular, 4-edge-connected graph having an…

math.CO2022

The limit in the $(k + 2, k)$ -Problem of Brown, Erdős and Sós exists for all $k \geq 2$

Michelle Delcourt, Luke Postle

Let $f^{(r)} (n; s, k)$ be the maximum number of edges of an $r$ -uniform hypergraph on~ $n$ vertices not containing a subgraph with $k$ ~edges and at most $s$ ~vertices. In 1973, Brown,…

math.CO2022

Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings

Michelle Delcourt, Luke Postle

In 1973, Erdős conjectured the existence of high girth $(n, 3, 2)$ -Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate v…

math.CO2021★ 8 cited

Reducing Linear Hadwiger's Conjecture to Coloring Small Graphs

Michelle Delcourt, Luke Postle

In 1943, Hadwiger conjectured that every graph with no $K_{t}$ minor is $(t - 1)$ -colorable for every $t \geq 1$ . In the 1980s, Kostochka and Thomason independently proved that every gra…

math.CO2020

Generalized rainbow Turán numbers of odd cycles

József Balogh, Michelle Delcourt, Emily Heath +1

Given graphs $F$ and $H$ , the generalized rainbow Turán number $ex (n, F, rainbow- H)$ is the maximum number of copies of $F$ in an $n$ -vertex graph with a proper edge-co…

math.CO2020★ 1 cited

Edge-colouring graphs with local list sizes

Marthe Bonamy, Michelle Delcourt, Richard Lang +1

The famous List Colouring Conjecture from the 1970s states that for every graph $G$ the chromatic index of $G$ is equal to its list chromatic index. In 1996 in a seminal paper, Kah…

math.CO2019

Progress towards Nash-Williams' Conjecture on Triangle Decompositions

Michelle Delcourt, Luke Postle

Partitioning the edges of a graph into edge disjoint triangles forms a triangle decomposition of the graph. A famous conjecture by Nash-Williams from 1970 asserts that any sufficie…

cs.DS2018

The Glauber dynamics for edge-colourings of trees

Michelle Delcourt, Marc Heinrich, Guillem Perarnau

Let $T$ be a tree on $n$ vertices and with maximum degree $Δ$ . We show that for $k \geq Δ + 1$ the Glauber dynamics for $k$ -edge-colourings of $T$ mixes in polynomial time in $n$ . The…

cs.DS2018★ 2 cited

Improved Bounds for Randomly Sampling Colorings via Linear Programming

Sitan Chen, Michelle Delcourt, Ankur Moitra +2

A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of $k$ -colorings of a graph $G$ on $n$ vertices with maximum degree $Δ$ is r…

math.CO2018

Independent Sets in Algebraic Hypergraphs

Anton Bernshteyn, Michelle Delcourt, Anush Tserunyan

In this paper we study hypergraphs definable in an algebraically closed field. Our goal is to show, in the spirit of the so-called transference principles in extremal combinatorics…

cs.DM2018★ 4 cited

Rapid mixing of Glauber dynamics for colorings below Vigoda's $11/6$ threshold

Michelle Delcourt, Guillem Perarnau, Luke Postle

A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of $k$ -colorings of a graph $G$ on $n$ vertices with maximum degree $Δ$ is r…

math.CO2018

A short nonalgorithmic proof of the containers theorem for hypergraphs

Anton Bernshteyn, Michelle Delcourt, Henry Towsner +1

Recently the breakthrough method of hypergraph containers, developed independently by Balogh, Morris, and Samotij as well as Saxton and Thomason, has been used to study sparse rand…

A Proof of Nash-Williams' Conjecture

Fractional Clique Decompositions of Dense Hypergraphs

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

Erdős meets Nash-Williams

A Short Proof of the Existence of Kqr​-absorbers

Sunflowers in set systems with small VC-dimension

Thresholds for (n,q,2)-Steiner Systems via Refined Absorption

Clique Decompositions in Random Graphs via Refined Absorption

Proof of the High Girth Existence Conjecture via Refined Absorption

Refined Absorption: A New Proof of the Existence Conjecture

Decomposing random regular graphs into stars

On generalized Ramsey numbers in the non-integral regime

Almost all 9-regular graphs have a modulo-5 orientation

The limit in the (k+2,k)-Problem of Brown, Erdős and Sós exists for all k≥2

Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings

Reducing Linear Hadwiger's Conjecture to Coloring Small Graphs

Generalized rainbow Turán numbers of odd cycles

Edge-colouring graphs with local list sizes

Progress towards Nash-Williams' Conjecture on Triangle Decompositions

The Glauber dynamics for edge-colourings of trees

Improved Bounds for Randomly Sampling Colorings via Linear Programming

Independent Sets in Algebraic Hypergraphs

Rapid mixing of Glauber dynamics for colorings below Vigoda's 11/6 threshold

A short nonalgorithmic proof of the containers theorem for hypergraphs

A Short Proof of the Existence of $K_{q}^{r}$ -absorbers

Thresholds for $(n, q, 2)$ -Steiner Systems via Refined Absorption

The limit in the $(k + 2, k)$ -Problem of Brown, Erdős and Sós exists for all $k \geq 2$

Rapid mixing of Glauber dynamics for colorings below Vigoda's $11/6$ threshold