How to eat 4/9 of a pizza
  Given two players alternately picking pieces of a pizza sliced by radial cuts, in such a way that after the first piece is taken every subsequent chosen piece is adjacent to some previously taken piece, we provide a strategy for the starting player to get 4/9 of the pizza. This is best possible and settles a conjecture of Peter Winkler. 
Kolja Knauer, Piotr Micek, Torsten Ueckerdt