A Polynomial Kernel for Funnel Arc Deletion Set

Abstract In Directed Feedback Arc Set ( DFAS ) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is well-known open problem parameterized complexity to decide if admits kernel polynomial size. We consider $$\mathcal {C}$$ C - Deletion ADS ), variant where want remove from digraph order turn it into class . this work, choose be funnels Funnel NP-hard even DAG, but fixed-parameter tractable with respect So far no kernels were known. Our main result {O}(k^6)$$ O ( k 6 ) many vertices and {O}(k^7)$$ 7 arcs, computable {O}(nm)$$ n m time, n number m