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A parameterized perspective on packing paths of length two

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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 \(\mathcal{O}^{*}(2.448^{3k})\) .

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Authors and Affiliations

  1. FB IV—Abteilung Informatik, Universität Trier, 54286, Trier, Germany

    Henning Fernau & Daniel Raible

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  1. Henning Fernau
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  2. Daniel Raible
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Correspondence to Daniel Raible.

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Fernau, H., Raible, D. A parameterized perspective on packing paths of length two. J Comb Optim 18, 319–341 (2009). https://doi.org/10.1007/s10878-009-9230-0

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