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math.CO2025
Cycle-factors of regular graphs via entropy
Micha Christoph, Nemanja Draganić, 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 Draganić, 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(Δ+1)…
math.CO2024
Upper bounds for multicolour Ramsey numbers
Paul Balister, Béla Bollobás, Marcelo Campos +5
The -colour Ramsey number is the minimum such that every -colouring of the edges of the complete graph on vertices contains a monochroma…