81 citations · 836 across the 70 of their papers we have counts for
6 papers · 2 filters
Loose Hamilton cycles in hypergraphs
Peter Keevash, Daniela Kühn, Richard Mycroft +1
We prove that any k-uniform hypergraph on n vertices with minimum degree at least n/(2(k-1))+o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by Küh…
An Ore-type theorem for perfect packings in graphs
Daniela Kühn, Deryk Osthus, Andrew Treglown
We say that a graph G has a perfect H-packing (also called an H-factor) if there exists a set of disjoint copies of H in G which together cover all the vertices of G. Given a graph…
Hamiltonian degree sequences in digraphs
Daniela Kühn, Deryk Osthus, Andrew Treglown
We show that for each η>0 every digraph G of sufficiently large order n is Hamiltonian if its out- and indegree sequences d^+_1\le ... \le d^+_n and d^- _1 \le ... \le d^-_n satisf…
Cycles Of Given Length In Oriented Graphs
Luke Kelly, Daniela Kühn, Deryk Osthus
We show that for each \ell\geq 4 every sufficiently large oriented graph G with δ^+(G), δ^-(G) \geq \lfloor |G|/3 \rfloor +1 contains an \ell-cycle. This is best possible for all t…
Minors in random regular graphs
N. Fountoulakis, D. Kühn, D. Osthus
We show that there is a constant c>0 so that for any fixed r which is at least 3 a.a.s. an r-regular graph on n vertices contains a complete graph on c n^{1/2} vertices as a minor.…
An exact minimum degree condition for Hamilton cycles in oriented graphs
Peter Keevash, Daniela Kühn, Deryk Osthus
We show that every sufficiently large oriented graph with minimum in- and outdegree at least (3n-4)/8 contains a Hamilton cycle. This is best possible and solves a problem of Thoma…