Algorithmic aspects of \(k\)-tuple total domination in graphs

DOI10.1016/j.ipl.2012.07.010zbMath1248.68222OpenAlexW2028613978MaRDI QIDQ456136

J. Herrera, D. Rodríguez-Gómez

Publication date: 23 October 2012

Published in: Information Processing Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ipl.2012.07.010

zbMATH Keywords

graph algorithmsNP-completedominationAPX-completetotal domination\(k\)-tuple total domination

Mathematics Subject Classification ID

Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Graph algorithms (graph-theoretic aspects) (05C85) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Approximation algorithms (68W25)

Related Items (17)

Complexity of \(k\)-tuple total and total \(\{k\}\)-dominations for some subclasses of bipartite graphs ⋮ Algorithmic aspects of open neighborhood location-domination in graphs ⋮ Domination parameters with number 2: interrelations and algorithmic consequences ⋮ On the algorithmic complexity of \(k\)-tuple total domination ⋮ Complexity of total outer-connected domination problem in graphs ⋮ On upper bounds for total k-domination number via the probabilistic method ⋮ On the domination of triangulated discs ⋮ Liar's dominating set problem on unit disk graphs ⋮ Computing a minimum outer-connected dominating set for the class of chordal graphs ⋮ Global total \(k\)-domination: approximation and hardness results ⋮ Efficient self-stabilizing algorithms for minimal total \(k\)-dominating sets in graphs ⋮ Hardness results of global total \(k\)-domination problem in graphs ⋮ An efficient algorithm for distance total domination in block graphs ⋮ Total 2-domination of proper interval graphs ⋮ Unnamed Item ⋮ New algorithms for weighted \(k\)-domination and total \(k\)-domination problems in proper interval graphs ⋮ A simple optimal algorithm for \(k\)-tuple dominating problem in interval graphs

Cites Work

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• Classes of bipartite graphs related to chordal graphs
• Optimization, approximation, and complexity classes
• Some APX-completeness results for cubic graphs
• \(k\)-tuple total domination in cross products of graphs
• Incidence matrices and interval graphs
• A threshold of ln n for approximating set cover
• On the Algorithmic Complexity of Total Domination
• Dually Chordal Graphs

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