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ISAAC

2009

Springer

2009

Springer

For a connected graph G = (V, E), a subset U ⊆ V is called a k-cut if U disconnects G, and the subgraph induced by U contains exactly k (≥ 1) components. More speciﬁcally, a k-cut U is called a (k, ℓ)-cut if V \U induces a subgraph with exactly ℓ (≥ 2) components. We study two decision problems, called k-Cut and (k, ℓ)-Cut, which determine whether a graph G has a k-cut or (k, ℓ)-cut, respectively. By pinpointing a close relationship to graph contractibility problems we ﬁrst show that (k, ℓ)-Cut is in P for k = 1 and any ﬁxed constant ℓ ≥ 2, while the problem is NP-complete for any ﬁxed pair k, ℓ ≥ 2. We then prove that k-Cut is in P for k = 1, and is NP-complete for any ﬁxed k ≥ 2. On the other hand, we present an FPT algorithm that solves (k, ℓ)-Cut on apex-minor-free graphs when parameterized by k + ℓ. By modifying this algorithm we can also show that k-Cut is in FPT (with parameter k) and Disconnected Cut is solvable in polynomial time for ape...

Related Content

Added |
25 Jul 2010 |

Updated |
25 Jul 2010 |

Type |
Conference |

Year |
2009 |

Where |
ISAAC |

Authors |
Takehiro Ito, Marcin Kaminski, Daniël Paulusma, Dimitrios M. Thilikos |

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