Turing kernelization for finding long paths and cycles in restricted graph classes

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9 Citaten (Scopus)

Samenvatting

The k-PATH problem asks whether a given undirected graph has a (simple) path of length k. We prove that k-PATH has polynomial-size Turing kernels when restricted to planar graphs, graphs of bounded degree, claw-free graphs, or to K 3,t-minor-free graphs. This means that there is an algorithm that, given a k-PATH instance (G,k) belonging to one of these graph classes, computes its answer in polynomial time when given access to an oracle that solves k-PATH instances of size polynomial in k in a single step. Our techniques also apply to k-CYCLE, which asks for a cycle of length at least k.

Originele taal-2Engels
Pagina's (van-tot)18-37
Aantal pagina's20
TijdschriftJournal of Computer and System Sciences
Volume85
DOI's
StatusGepubliceerd - mei 2017

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