76 citations · 568 across the 46 of their papers we have counts for
47 papers · 1 filter
Canonical colourings in random graphs
Nina Kamčev, Mathias Schacht
Rödl and Ruciński (1990) established Ramsey's theorem for random graphs. In particular, for fixed integers , they showed that $\hat p_{K_\ell,r}(n)=n^{-\frac{2}{\el…
Sharp thresholds for Ramsey properties
Ehud Friedgut, Eden Kuperwasser, Wojciech Samotij +1
In this work, we develop a unified framework for establishing sharp threshold results for various Ramsey properties. To achieve this, we view such properties as non-colourability o…
Turán density of cliques of order five in -uniform hypergraphs with quasirandom links
Sören Berger, Simón Piga, Christian Reiher +2
We show that -uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than contain a clique on five vertices. This result…
On quantitative aspects of a canonisation theorem for edge-orderings
Christian Reiher, Vojtěch Rödl, Marcelo Sales +2
For integers and there are canonical orderings of the edges of the complete -uniform hypergraph with vertex set . These are…
Localised codegree conditions for tight Hamilton cycles in 3-uniform hypergraphs
Pedro Araújo, Simón Piga, Mathias Schacht
We study sufficient conditions for the existence of Hamilton cycles in uniformly dense -uniform hypergraphs. Problems of this type were first considered by Lenz, Mubayi, and Myc…
Minimum pair degree condition for tight Hamiltonian cycles in -uniform hypergraphs
Joanna Polcyn, Christian Reiher, Vojtěch Rödl +3
We show that every 4-uniform hypergraph with vertices and minimum pair degree at least contains a tight Hamiltonian cycle. This degree condition is asymptotic…