On the Complexity of the 3-Kernel Problem in Some Classes of Digraphs

• Autorzy: Pavol Hell , César Hernández-Cruz
• Języki publikacji: EN

Abstrakty

EN

Let D be a digraph with the vertex set V (D) and the arc set A(D). A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v), d(v, u) ≥ k; it is l-absorbent if for every u ∈ V (D) − N there exists v ∈ N such that d(u, v) ≤ l. A k-kernel of D is a k-independent and (k − 1)-absorbent subset of V (D). A 2-kernel is called a kernel. It is known that the problem of determining whether a digraph has a kernel (“the kernel problem”) is NP-complete, even in quite restricted families of digraphs. In this paper we analyze the computational complexity of the corresponding 3-kernel problem, restricted to three natural families of digraphs. As a consequence of one of our main results we prove that the kernel problem remains NP-complete when restricted to 3-colorable digraphs.

Słowa kluczowe

EN

kernel; 3-kernel; NP-completeness; multipartite tournament; cyclically 3-partite digraphs; k-quasi-transitive digraph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 1
• Strony: 167-185

Daty

wydano

2014-02-01

online

2014-02-14

Twórcy

autor

Pavol Hell

• School of Computing Science Simon Fraser University Burnaby, B.C., Canada V5A 1S6

autor

César Hernández-Cruz

• School of Computing Science Simon Fraser University Burnaby, B.C., Canada V5A 1S6

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Identyfikatory

DOI

10.7151/dmgt.1727