Luke Postle

activity

20242026

collaborators

8 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

Refined Absorption: A New Proof of the Existence Conjecture and its Applications to Extremal and Probabilistic Design Theory

Luke Postle

We discuss the recently developed method of refined absorption and how it is used to provide a new proof of the Existence Conjecture for combinatorial designs. This method can also…

math.CO2025

The chromatic number of triangle-free hypergraphs

Lina Li, Luke Postle

A triangle in a hypergraph $H$ is a set of three distinct edges $e, f, g \in H$ and three distinct vertices $u, v, w \in V (H)$ such that $\{u, v\}\subset…

math.CO2025

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.CO2025

11/4-colorability of subcubic triangle-free graphs

ZdenÄk DvoÅÃ¡k, Bernard LidickÃ½, Luke Postle

We prove that up to two exceptions, every connected subcubic triangle-free graph has fractional chromatic number at most 11/4. This is tight unless further exceptional graphs are e…

math.CO2024

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…