11 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…
Fractional Clique Decompositions of Dense Hypergraphs
Michelle Delcourt, Thomas Lesgourgues, Luke Postle
In 2014, Keevash famously proved the existence of -Steiner systems as part of settling the Existence Conjecture of Combinatorial Designs (dating from the mid-1800s). In 20…
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 -divisible graph on vertices (for large enough) with minimum degree…
Erdős meets Nash-Williams
Michelle Delcourt, Cicely, Henderson +2
In 1847, Kirkman proved that there exists a Steiner triple system on vertices (equivalently a triangle decomposition of the edges of ) whenever satisfies the necessary…
A Short Proof of the Existence of -absorbers
Michelle Delcourt, Tom Kelly, Luke Postle
We codify a short self-contained proof of the existence of -absorbers implicit in Keevash's original proof of the Existence Conjecture. Combining this with the work of the f…
Generalized rainbow Turán numbers of odd cycles
József Balogh, Michelle Delcourt, Emily Heath +1
Given graphs and , the generalized rainbow Turán number is the maximum number of copies of in an -vertex graph with a proper edge-co…