Scattered packings of cycles

Aistis Atminas (1) , Marcin Kamiński (2) , Jean-Florent Raymond (2, 3)

1 Department of Mathematics, University of Warwick
2 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
3 ALGCO - Algorithmes, Graphes et Combinatoire

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.

Keywords: cycle packing; kernelization; multivariate algorithms; induced structures

Domains: Discrete Mathematics [cs.DM]

Aistis Atminas, Marcin Kamiński, Jean-Florent Raymond. Scattered packings of cycles. Theoretical Computer Science, 2016, 647, pp.33 - 42. ⟨10.1016/j.tcs.2016.07.021⟩. ⟨hal-01401905⟩