Directed graphs without short cycles Jacob Fox Peter Keevash Benny Sudakov Abstract For a directed graph without loops or parallel edges let denote the size of the smallest feedback arc set i

e the smallest subset such that has no directed cycles Let be the number of unordered pairs of vertices of which are not adjacent We prove that every directed graph whose shortest directed cycle has length at l east 4 satis64257es c r where is an a

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