Luke Postle

collaborators

5 papers

math.CO2026

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

On the Hypergraph Nash-Williams' Conjecture

Cicely Henderson, Luke Postle

In 2014, Keevash proved the existence of $(n, q, r)$ -Steiner systems (equivalently $K_{q}^{r}$ -decompositions of $K_{n}^{r}$ ) for all large enough $n$ satisfying the necessary divisibility c…

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

ErdÅs 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

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…

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

On the Hypergraph Nash-Williams' Conjecture

Fractional Clique Decompositions of Dense Hypergraphs

ErdÅs meets Nash-Williams

A Short Proof of the Existence of Kqr​-absorbers

ErdÅs meets Nash-Williams

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