# On the parameterized complexity of finding separators with non-hereditary properties

Heggernes, P and T, Hof and Marx, Dániel and Misra, N and Villanger, Y
(2012)
*On the parameterized complexity of finding separators with non-hereditary properties.*
In: Lecture notes in computer science, 2011-11-30, Jerusalem, Izrael.
10.1007/978-3-642-34611-8_33

## Abstract

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan 1985), while for example the problems of finding a minimum s-t separator that is a connected graph or an independent set are fixed-parameter tractable (Marx, O'Sullivan and Razgon, manuscript). We extend these results the following way: Finding a minimum c-connected s-t separator is FPT for c∈=∈2 and W[1]-hard for any c∈≥∈3. Finding a minimum s-t separator with diameter at most d is W[1]-hard for any d∈≥∈2. Finding a minimum r-regular s-t separator is W[1]-hard for any r∈≥∈1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. We also show that finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless NP ⊆ coNP/poly. © 2012 Springer-Verlag Berlin Heidelberg.

Item Type: | Conference or Workshop Item (-) |
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Uncontrolled Keywords: | Separators, Graph theory, Computer science, Polynomial-time, Polynomial kernels, Parameterized complexity, Parameterized, Maximum degree, Independent set, Graph properties, Connected graph |

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

Depositing User: | EPrints Admin |

Date Deposited: | 16 Jan 2014 10:30 |

Last Modified: | 05 Feb 2014 12:27 |

URI: | https://eprints.sztaki.hu/id/eprint/7380 |

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