# Parameterized vertex deletion problems for hereditary graph classes with a block property

Bonnet, Édouard and Brettel, Nick and Kwon, O-joung and Marx, Dániel
(2016)
*Parameterized vertex deletion problems for hereditary graph classes with a block property.*
LECTURE NOTES IN ARTIFICIAL INTELLIGENCE, 9941 L.
pp. 233-244.
ISSN 0302-9743
10.1007/978-3-662-53536-3_20

Text
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## Abstract

For a class of graphs P, the Bounded P-Block Vertex Deletion problem asks, given a graph G on n vertices and positive integers k and d, whether there is a set S of at most k vertices such that each block of G − S has at most d vertices and is in P. We show that when P satisfies a natural hereditary property and is recognizable in polynomial time, Bounded P-Block Vertex Deletion can be solved in time 2O(k log d)nO(1), and this running time cannot be improved to 2o(k log d)nO(1), in general, unless the Exponential Time Hypothesis fails. On the other hand, if P consists of only complete graphs, or only K1,K2, and cycle graphs, then Bounded P-Block Vertex Deletion admits a cknO(1)-time algorithm for some constant c independent of d. We also show that Bounded P-Block Vertex Deletion admits a kernel with O(k2d7) vertices. © Springer-Verlag GmbH Germany 2016.

Item Type: | Article |
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Uncontrolled Keywords: | Graph theory; Vertex deletion problems; Time algorithms; Positive integers; Polynomial-time; Hereditary property; Exponential time hypothesis; Complete graphs; Block properties; Polynomial approximation |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Divisions: | Informatics Laboratory |

SWORD Depositor: | MTMT Injector |

Depositing User: | MTMT Injector |

Date Deposited: | 29 Jan 2017 20:33 |

Last Modified: | 29 Jan 2017 20:33 |

URI: | http://eprints.sztaki.hu/id/eprint/9042 |

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