81 citations · 836 across the 70 of their papers we have counts for
6 papers · 1 filter
A proof of Sumner's universal tournament conjecture for large tournaments
Daniela Kühn, Richard Mycroft, Deryk Osthus
Sumner's universal tournament conjecture states that any tournament on vertices contains any directed tree on vertices. In this paper we prove that this conjecture holds…
An approximate version of Sumner's universal tournament conjecture
Daniela Kühn, Richard Mycroft, Deryk Osthus
Sumner's universal tournament conjecture states that any tournament on vertices contains a copy of any directed tree on vertices. We prove an asymptotic version of this…
Matchings in 3-uniform hypergraphs
Daniela Kühn, Deryk Osthus, Andrew Treglown
We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose that H is a sufficiently large 3-uniform hypergraph whose…
A survey on Hamilton cycles in directed graphs
Daniela Kühn, Deryk Osthus
We survey some recent results on long-standing conjectures regarding Hamilton cycles in directed graphs, oriented graphs and tournaments. We also combine some of these to prove the…
Approximate Hamilton Decompositions of Random Graphs
Fiachra Knox, Daniela Kühn, Deryk Osthus
We show that if pn >> log n, the binomial random graph G_{n,p} has an approximate Hamilton decomposition. More precisely, we show that in this range G_{n,p} contains a set of edge-…
A semi-exact degree condition for Hamilton cycles in digraphs
Demetres Christofides, Peter Keevash, Daniela Kühn +1
The paper is concerned with directed versions of Posa's theorem and Chvatal's theorem on Hamilton cycles in graphs. We show that for each a>0, every digraph G of sufficiently large…