On the Small Cycle Transversal of Planar Graphs

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On the Small Cycle Transversal of Planar Graphs
We consider the problem of finding a k-edge transversal set that covers all (simple) cycles of length at most s in a planar graph, where s ≥ 3 is a constant. This problem, referred to as Small Cycle Transversal, is known to be NP-complete. We present a polynomial-time algorithm that computes a linear kernel of size 36s3 k for Small Cycle Transversal. In order to achieve this kernel, we extend the region decomposition technique of Alber et al. [J. ACM, 2004 ] by considering a unique region decomposition that is defined by shortest paths. Unlike the previous results on linear kernels of problems on planar graphs, our results are not subsumed by the recent meta-theorems on kernelization of Bodlaender et al. [FOCS, 2009 ].
Ge Xia, Yong Zhang
Added 31 Jan 2011
Updated 31 Jan 2011
Type Journal
Year 2010
Where WG
Authors Ge Xia, Yong Zhang
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