On $3$-uniform hypergraphs without linear cycles
  We explore properties of $3$-uniform hypergraphs $H$ without linear cycles. Our main results are that these hypergraphs must contain a vertex of strong degree at most two and must have independent sets of size at least ${2|V(H)|\over 5}$. 
Andr\'as Gy\'arf\'as, Ervin Gy\H{o}ri and Mikl\'os Simonovits
math.CO