A Parameterized Perspective on $P_2$-Packings

Details A Parameterized Perspective on $P_2$-Packings A Parameterized Perspective on $P_2$-Packings

2008-04-03

arxiv.org/abs/0804.0570v1

Computer Science

Data Structures and Algorithms

Scientific paper

}We study (vertex-disjoint) $P_2$-packings in graphs under a parameterized perspective. Starting from a maximal $P_2$-packing $\p$ of size $j$ we use extremal arguments for determining how many vertices of $\p$ appear in some $P_2$-packing of size $(j+1)$. We basically can 'reuse' $2.5j$ vertices. We also present a kernelization algorithm that gives a kernel of size bounded by $7k$. With these two results we build an algorithm which constructs a $P_2$-packing of size $k$ in time $\Oh^*(2.482^{3k})$.

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