81 citations · 836 across the 70 of their papers we have counts for
5 papers · 2 filters
Optimal packings of Hamilton cycles in graphs of high minimum degree
Daniela Kühn, John Lapinskas, Deryk Osthus
We study the number of edge-disjoint Hamilton cycles one can guarantee in a sufficiently large graph G on n vertices with minimum degree d = (1/2+a)n. For any constant a > 0, we gi…
On Posa's conjecture for random graphs
Daniela Kühn, Deryk Osthus
The famous Posa conjecture states that every graph of minimum degree at least 2n/3 contains the square of a Hamilton cycle. This has been proved for large n by Komlós, Sarközy and…
Optimal covers with Hamilton cycles in random graphs
Dan Hefetz, Daniela Kühn, John Lapinskas +1
A packing of a graph G with Hamilton cycles is a set of edge-disjoint Hamilton cycles in G. Such packings have been studied intensively and recent results imply that a largest pack…
Hamilton decompositions of regular expanders: applications
Daniela Kühn, Deryk Osthus
In a recent paper, we showed that every sufficiently large regular digraph G on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into ed…
Hamilton decompositions of regular expanders: a proof of Kelly's conjecture for large tournaments
Daniela Kühn, Deryk Osthus
A long-standing conjecture of Kelly states that every regular tournament on n vertices can be decomposed into (n-1)/2 edge-disjoint Hamilton cycles. We prove this conjecture for la…