6 papers
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…
Odd-Ramsey numbers of Hamilton cycles
Simona Boyadzhiyska, Shagnik Das, Thomas Lesgourgues +1
The odd-Ramsey number of a graph , as introduced by Alon in his work on graph-codes, is the minimum number of colours needed to edge-colour so that ev…
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…
ErdÅs 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…
Ramsey with purple edges
Thomas Lesgourgues, Anita Liebenau, Nye Taylor
Motivated by a question of Angell, we investigate a variant of Ramsey numbers where some edges are coloured simultaneously red and blue, which we call purple. Specifically, we are…
Odd-Ramsey numbers of complete bipartite graphs
Simona Boyadzhiyska, Shagnik Das, Thomas Lesgourgues +1
In his study of graph codes, Alon introduced the concept of the odd-Ramsey number of a family of graphs in , defined as the minimum number of colours needed to c…