3 papers
math.CO2026
Monochromatic cycle partitions of -edge-coloured graphs with high minimum degree
Francesco Di Braccio, Viresh Patel
A question posed independently by Letzter and Pokrovskiy asks: how many vertex-disjoint monochromatic cycles are needed to cover the vertex set of an -edge-coloured graph, as a…
math.CO2025
Hamilton decompositions of regular tripartite tournaments
Francesco Di Braccio, Joanna Lada, Viresh Patel +2
Kühn and Osthus conjectured in 2013 that regular tripartite tournaments are decomposable into Hamilton cycles. Somewhat surprisingly, Granet gave a simple counterexample to this co…
math.CO2025
Leaf-to-leaf paths of many lengths
Francesco Di Braccio, Kyriakos Katsamaktsis, Alexandru Malekshahian
We prove that every tree of maximum degree with leaves contains paths between leaves of at least distinct lengths. This settles in a strong form…