A 5k kernel for P2-packing in net-free graphs

Given a graph G = (V, E), a P 2 -packing P is a collection of vertex disjoint copies of P 2 s in G where a P 2 is a simple path with three vertices and two edges. The kP 2 -Packing problem asks whether there exists a P 2 -packing of size k in G by taking graph G and a fixed parameter k as the input....

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Bibliographic Details
Published in:ICSEC : 2014 International Computer Science and Engineering Conference : July 30, 2014-August 1, 2014 pp. 12 - 17
Main Authors: Maw-Shang Chang, Li-Hsuan Chen, Ling-Ju Hung
Format: Conference Proceeding
Language:English
Published: IEEE 01.07.2014
Subjects:
Algorithm design and analysis
Bipartite graph
Computer science
Educational institutions
Kernel
kernelization algorithm
net-free graphs
P 2 -packing
Particle separators
Polynomials
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Summary:Given a graph G = (V, E), a P 2 -packing P is a collection of vertex disjoint copies of P 2 s in G where a P 2 is a simple path with three vertices and two edges. The kP 2 -Packing problem asks whether there exists a P 2 -packing of size k in G by taking graph G and a fixed parameter k as the input. This problem is NP-hard for net-free graphs. In this paper, we give a kernelization algorithm for the kP 2 -Packing problem in net-free graphs. We show that in polynomial time our kernelization algorithm obtains a size-5k kernel which is smaller than those kernels found by previous known kernelization algorithms.
DOI:10.1109/ICSEC.2014.6978121