3 papers
math.CO2025
Cycle-factors of regular graphs via entropy
Micha Christoph, Nemanja DraganiÄ, António Girão +3
It is a classical result that a random permutation of elements has, on average, about cycles. We generalise this fact to all directed -regular graphs on vertice…
math.CO2025
New bounds for linear arboricity and related problems
Micha Christoph, Nemanja DraganiÄ, António Girão +3
A linear forest is a collection of vertex-disjoint paths. The Linear Arboricity Conjecture states that every graph of maximum degree can be decomposed into at most $\lceil(Î+…
math.CO2024
Exponential odd-distance sets under the Manhattan metric
Alberto Espuny DÃaz, Emma Hogan, Freddie Illingworth +3
We construct a set of points in such that all pairwise Manhattan distances are odd integers, which improves the recent linear lower bound of Golovanov, Kupavsk…