Abstract
The arboricity of a hypergraph
H
is the minimum number of acyclic hypergraphs that partition
H
. The determination of the arboricity of hypergraphs is a problem motivated by database theory. The exact arboricity of the complete
k
-uniform hypergraph of order
n
is previously known only for
k
∈
{
1
,
2
,
n
−
2
,
n
−
1
,
n
}
. The arboricity of the complete
k
-uniform hypergraph of order
n
is determined asymptotically when
k
=
n
−
O
(
log
1
−
δ
n
)
,
δ
positive, and determined exactly when
k
=
n
−
3
. This proves a conjecture of Wang (2008)
[20] in the asymptotic sense.
► We study the arboricity of hypergraphs, the minimum number of acyclic hypergraphs that partition a given hypergraph. ► The arboricity of the complete
k
-uniform hypergraph is determined when
k
=
n
−
3
. ► The arboricity of the complete
k
-uniform hypergraph of order
n
is determined asymptotically when
k
=
n
=
O
(
log
1
−
δ
n
)
,
δ
positive.