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A parameterized perspective on packing paths of length two

Author

Listed:
  • Henning Fernau

    (Universität Trier)

  • Daniel Raible

    (Universität Trier)

Abstract

We study (vertex-disjoint) packings of paths of length two (i.e., of P 2’s) in graphs under a parameterized perspective. Starting from a maximal P 2-packing ℘ of size j we use extremal combinatorial arguments for determining how many vertices of ℘ appear in some P 2-packing of size (j+1) (if such a packing exists). We prove that one can ‘reuse’ 2.5j vertices. We also show that this bound is asymptotically sharp. Based on a WIN-WIN approach, we build an algorithm which decides, given a graph, if a P 2-packing of size at least k exists in time $\mathcal{O}^{*}(2.448^{3k})$ .

Suggested Citation

  • Henning Fernau & Daniel Raible, 2009. "A parameterized perspective on packing paths of length two," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 319-341, November.
    • Handle: RePEc:spr:jcomop:v:18:y:2009:i:4:d:10.1007_s10878-009-9230-0
    DOI: 10.1007/s10878-009-9230-0
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    Cited by:

    1. Wenying Xi & Wensong Lin, 2021. "On maximum $$P_3$$ P 3 -packing in claw-free subcubic graphs," Journal of Combinatorial Optimization, Springer, vol. 41(3), pages 694-709, April.
    2. Maw-Shang Chang & Li-Hsuan Chen & Ling-Ju Hung, 2016. "An $$O^{*}(1.4366^n)$$ O ∗ ( 1 . 4366 n ) -time exact algorithm for maximum $$P_2$$ P 2 -packing in cubic graphs," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 594-607, August.
    3. Qilong Feng & Jianxin Wang & Shaohua Li & Jianer Chen, 2015. "Randomized parameterized algorithms for $$P_2$$ P 2 -Packing and Co-Path Packing problems," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 125-140, January.

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