13 citations · 115 across the 49 of their papers we have counts for
66 papers
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 vertices (for large enough) with minimum deg…
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…
Acyclic List Colouring Locally Planar Graphs
Luke Postle, Evelyne Smith-Roberge, Massimo Vicenzo
A (vertex) colouring of graph is \emph{acyclic} if it contains no bicoloured cycle. In 1979, Borodin proved that planar graphs are acyclically 5-colourable. In 2010, Kawarabayashi…
Clique Decompositions in Random Graphs via Refined Absorption
Michelle Delcourt, Tom Kelly, Luke Postle
We prove that if for some , then asymptotically almost surely the binomial random graph has a -packing containing all but at most $n +…
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…
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…