Planar Digraphs of Digirth Four are 2-Colorable

Abstract

Neumann-Lara conjectured in 1985 that every planar digraph with digirth at least three is 2-colorable, meaning that the vertices can be 2-colored without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least four is 2-colorable.