Planar digraphs of digirth five are 2-colorable
  Neumann-Lara (1985) and \v{S}krekovski conjectured that every planar digraph with digirth at least three is 2-colorable. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2-colorable. The result also holds in the setting of list colorings. 
Ararat Harutyunyan and Bojan Mohar
math.CO