REVIEW 1 cited by
Loose Hamilton Cycles in Random Uniform Hypergraphs
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
In the random hypergraph $H_{n,p;k}$ each possible $k$-tuple appears independently with probability $p$. A loose Hamilton cycle is a cycle in which every pair of adjacent edges intersects in a single vertex. We prove that if $p n^{k-1}/\log n$ tends to infinity with $n$ then $$\lim_{\substack{n\to \infty 2(k-1) |n}}\Pr(H_{n,p;k}\ contains\ a\ loose\ Hamilton\ cycle)=1.$$ This is asymptotically best possible.
Forward citations
Cited by 1 Pith paper
-
Sharp Thresholds for Factors in Random Graphs
For every strictly 1-balanced graph F, the random graph G(n,p) gets an F-factor exactly at the sharp threshold where F-isolated vertices vanish, confirming Ruciński's conjecture.
Discussion (0). Continue with ORCID to comment.