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The Grid Theorem of Robertson and Seymour [JCTB, 1986], is one of the most important tools in the field of structural graph theory, finding numerous applications in the design of algorithms for undirected graphs. An analogous version of the Grid Theorem in digraphs was conjectured by Johnson et al. [JCTB, 2001], and proved by Kawarabayashi and Kreutzer [STOC, 2015]. Namely, they showed that there is a function f(k) such that every digraph of directed tree-width at least f(k) contains aarXiv:2007.07738v2 fatcat:6y47msh25jgnrntrjh4tru66ke