Abstract
The \(P_2\)-packing problem asks for whether a graph contains k vertex-disjoint paths each of length two. We continue the study of its kernelization algorithms, and develop a 5k-vertex kernel.
Supported in part by NSFC under grant 61502054, RGC under grant PolyU 252026/15E, NSFC under grant 61572414, Natural Science Foundation of Hunan Province under grant 2017JJ3333 and Scientific Research Fund of Hunan Provincial Education Department under grant 17C0047.
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Notes
- 1.
One may define the reducible set in a way that an edge component is regarded as two single-vertex components. This definition might reveal more reducible sets. However, it would slightly complicate our presentation without helping our analysis in the worst case, and hence we choose to use the simpler one.
- 2.
Proofs of propositions marked with \(*\) are omitted due to space limit.
- 3.
Actually, when neither \(U_1\) nor \(U_2\) is a (1, 4)-unit, we can move vertices in an arbitrary direction. We choose this way to simplify our proof.
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Li, W., Ye, J., Cao, Y. (2018). Kernelization for \(P_2\)-Packing: A Gerrymandering Approach. In: Chen, J., Lu, P. (eds) Frontiers in Algorithmics. FAW 2018. Lecture Notes in Computer Science(), vol 10823. Springer, Cham. https://doi.org/10.1007/978-3-319-78455-7_11
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