3 papers
math.CO2025
A proof of a conjecture of ErdÅs and Gyárfás on monochromatic path covers
Alexey Pokrovskiy, Leo Versteegen, Ella Williams
In 1995, ErdÅs and Gyárfás proved that in every -edge-coloured complete graph on vertices, there exists a collection of monochromatic paths, all of the same c…
math.CO2025
The sandglass conjecture beyond cancellative pairs
Adva Mond, Victor Souza, Leo Versteegen
The sandglass conjecture, posed by Simonyi, states that if a pair of families of subsets of is recovering then . We improve the best known upper bo…
math.CO2024
On norming systems of linear equations
Seokjoon Cho, David Conlon, Joonkyung Lee +2
A system of linear equations is said to be norming if a natural functional giving a weighted count for the set of solutions to the system can be used to define a n…