Scattered packings of cycles
Résumé
We consider the problem Scattered Cycles which, given a graph G and two positive integers r and , asks whether G contains a collection of r cycles that are pairwise at distance at least. This problem generalizes the problem Disjoint Cycles which corresponds to the case = 1. We prove that when parameterized by r, , and the maximum degree ∆, the problem Scattered Cycles admits a kernel on 24 2 ∆ r log(8 2 ∆ r) vertices. We also provide a (16 2 ∆)-kernel for the case r = 2 and a (148∆r log r)-kernel for the case = 1. Our proofs rely on two simple reduction rules and a careful analysis.
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