2 problems

Matching

The characterization conjecture for $F$ -factors in $k$ -uniform hypergraphs
The characterization conjecture. The $k$ -graph $F$ belongs to $\textbf{FACTOR}_k$ if and only if it satisfies:
openextremal-combinatorics hypergraph-factors quasi-random-hypergraphs
08
Minimum codegree conjecture for loose cycle factors
Loose-cycle factor conjecture. If $n$ is sufficiently large and
openhypergraph-factors loose-cycles minimum-codegree
06