Robust domination in random graphs

Ghurumuruhan Ganesan ()
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Ghurumuruhan Ganesan: IISER Bhopal

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 427-438

Abstract: Abstract In this paper, we study “robust” dominating sets of random graphs that retain the domination property even if a small deterministic set of edges are removed. We motivate our study by illustrating with examples from wireless networks in harsh environments. We then use the probabilistic method and martingale difference techniques to determine sufficient conditions for the asymptotic optimality of the robust domination number. We also discuss robust domination in sparse random graphs where the number of edges grows at most linearly in the number of vertices.

Keywords: Random Graphs; Robust Domination; Sparse Regime; 06C05; 05C62 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00374-6

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