27 research outputs found
Tight Hamilton Cycles in Random Uniform Hypergraphs
In this paper we show that is the sharp threshold for the existence of
tight Hamilton cycles in random -uniform hypergraphs, for all . When
we show that is an asymptotic threshold. We also determine
thresholds for the existence of other types of Hamilton cycles.Comment: 9 pages. Updated to add materia
The threshold for powers of tight Hamilton cycles in random hypergraphs
We investigate the occurrence of powers of tight Hamilton cycles in random
hypergraphs. For every and , we show that there exists a
constant such that if then
asymptotically almost surely the random hypergraph contains the
th power of a tight Hamilton cycle. This improves on a result of Parczyk and
Person, who proved the same result under the assumption
using a second moment
argument