  A linear cycle in a hypergraph $H$ is a cyclic sequence of hyperedges such
that two consecutive hyperedges intersect in exactly one element and two
nonconsecutive hyperedges are disjoint and $\alpha(H)$ denotes the size of a
largest independent set of $H$. In this note, we show that the vertex set of
every $3$-uniform hypergraph $H$ can be covered by at most $\alpha(H)$ pairwise
edge-disjoint linear cycles (where we accept a vertex and a hyperedge as a
linear cycle), proving a weaker version of a conjecture of Gy\'arf\'as and
S\'ark\"ozy.
