Parameterizing cut sets in a graph by the number of their components

Takehiro Ito, Marcin Kamiński, Daniël Paulusma, Dimitrios M. Thilikos

研究成果: Conference contribution

4 被引用数 (Scopus)


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 apex-minor-free graphs. The latter problem asks if a graph has a k-cut for some k≥2.

ホスト出版物のタイトルAlgorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings
出版ステータスPublished - 2009
イベント20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States
継続期間: 2009 12 162009 12 18


名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
5878 LNCS


Other20th International Symposium on Algorithms and Computation, ISAAC 2009
国/地域United States
CityHonolulu, HI

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)


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