3 papers
math.CO2025
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…
math.CO2025
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…
math.CO2024
Clustered Colouring of Graph Products
Rutger Campbell, J. Pascal Gollin, Kevin Hendrey +5
A colouring of a graph has clustering if the maximum number of vertices in a monochromatic component equals . Motivated by recent results showing that many natural graph…