FPT algorithms are presented for cycle rank at most w on semi-complete digraphs in O(9^{(w+1)4^{w+2}} n^2) time via reduction to directed clique-width, plus an n^{O(w)} algorithm for minimum feedback arc set.
Graph classes through the lens of logic
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An FPT algorithm for cycle rank on semi-complete digraphs
FPT algorithms are presented for cycle rank at most w on semi-complete digraphs in O(9^{(w+1)4^{w+2}} n^2) time via reduction to directed clique-width, plus an n^{O(w)} algorithm for minimum feedback arc set.