UnivTrevesV1, Main, Exploration, bibRecord, 000F71

Offensive r-alliances in graphs

Identifieur interne : 000F71 ( Main/Exploration ); précédent : 000F70; suivant : 000F72

Offensive r-alliances in graphs

Auteurs : Henning Fernau [Allemagne] ; Juan A. Rodriguez [Espagne] ; José M. Sigarreta [Mexique]

Source :

Discrete applied mathematics [ 0166-218X ] ; 2009.

RBID : Pascal:09-0039477

Descripteurs français

Pascal (Inist)
- Vertex, Ensemble dominant, Complexité calcul, Informatique théorique, Optimisation, Combinatoire, 68R10, Graphe simple, Cardinalité.

English descriptors

KwdEn :
- Combinatorics, Computational complexity, Computer theory, Dominating set, Optimization, Vertex.

Abstract

Let G = (V, E) be a simple graph. For a nonempty setX ⊂ V, and a vertex v ∈ V, δX(ù) denotes the number of neighbors v has in X. A nonempty set S ⊂ V is an offensive r-alliance in G if δ_S(ù) ≥ δ_S(ù) + r, ∀ù ∈ a(S), where a(S) denotes the boundary ofS. An offensive r-alliance S is called global if it forms a dominating set. The global offensive r-alliance number of G, denoted by γ⁰_r(G), is the minimum cardinality of a global offensive r-alliance in G. We show that the problem of finding optimal (global) offensive r-alliances is NP-complete and we obtain several tight bounds on γ⁰_r(G).

Affiliations:

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to stream PascalFrancis, to step Curation: 000667
to stream PascalFrancis, to step Checkpoint: 000497
to stream Main, to step Merge: 001053
to stream Main, to step Curation: 000F71

Le document en format XML

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<front><div type="abstract" xml:lang="en">Let G = (V, E) be a simple graph. For a nonempty setX ⊂ V, and a vertex v ∈ V, δX(ù) denotes the number of neighbors v has in X. A nonempty set S ⊂ V is an offensive r-alliance in G if δ<sub>S</sub>
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Offensive r-alliances in graphs

Offensive r-alliances in graphs

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri