Induced Forests in Bipartite Planar Graphs
  Akiyama and Watanabe conjectured that every simple planar bipartite graph on $n$ vertices contains an induced forest on at least $5n/8$ vertices. We apply the discharging method to show that every simple bipartite planar graph on $n$ vertices contains an induced forest on at least $\lceil (4n+3)/7 \rceil$ vertices. 
Yan Wang, Qiqin Xie, Xingxing Yu
math.CO