A parameterized perspective on packing paths of length two

Henning Fernau () and Daniel Raible ()
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Henning Fernau: Universität Trier
Daniel Raible: Universität Trier

Journal of Combinatorial Optimization, 2009, vol. 18, issue 4, No 1, 319-341

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

Keywords: Path packing; Parameterized algorithms; Extremal combinatorics (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10878-009-9230-0

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