Luke Postle

activity

20102026

most citedImproving the Caro-Wei bound and applications to Turán stability

1 citations · 1 across the 6 of their papers we have counts for

collaborators

Showing 2025Show all

4 papers · 1 filter

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

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…