Overtwisted discs in planar open books
  Using open book foliations we show that an overtwisted disc in a planar open book can be put in a topologically nice position. As a corollary, we prove that a planar open book whose fractional Dehn twist coefficients grater than one for all the boundary components supports a tight contact structure. 
Tetsuya Ito and Keiko Kawamuro
math.GT math.SG