The dichromatic number of D, denoted by − → χ (D), is the smallest integer k such that D admits an acyclic k-coloring. We use mader χ (F ) to denote the smallest integer kWe extend octi digraphs to a larger class of digraphs and prove that it is Mader-perfect, which generalizes a result of Gishboliner, Steiner and Szabó [Dichromatic number and forced subdivisions, J. Comb. Theory, Ser. B 153 (2022) 1-30]. We also show that if K is a proper subdigraph of ↔ C 4 except for the digraph obtained from ↔ C 4 by deleting an arbitrary arc, then K is Mader-perfect.

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