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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2014 | 34 | 1 | 167-185

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

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.

EN

167-185

wydano
2014-02-01
online
2014-02-14

### Twórcy

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

### Bibliografia

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