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

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9 papers · 1 filter

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

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…

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

Improving the Caro-Wei bound and applications to Turán stability

Tom Kelly, Luke Postle

We prove that if $G$ is a graph and $f (v) \leq 1/ (d (v) + 1/2)$ for each $v \in V (G)$ , then either $G$ has an independent set of size at least $\sum_{v \in V (G)} f (v)$ or $G$ contains…

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.CO2010

Sub-exponentially many 3-colorings of triangle-free planar graphs

Arash Asadi, Zdenek Dvorak, Luke Postle +1

Thomassen conjectured that every triangle-free planar graph on n vertices has exponentially many 3-colorings, and proved that it has at least 2^[n^(1/12)/20000] distinct 3-coloring…

A Combinatorial Proof of Hilton's Conjecture and Beyond

On the Hypergraph 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

Improving the Caro-Wei bound and applications to Turán stability

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

Sub-exponentially many 3-colorings of triangle-free planar graphs

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

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