Robust Domination in Random Graphs
Probability
2023-01-16 v1
Abstract
In this paper, we study "robust" dominating sets of random graphs that retain the domination property even if a small \emph{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.
Cite
@article{arxiv.2301.05386,
title = {Robust Domination in Random Graphs},
author = {Ghurumuruhan Ganesan},
journal= {arXiv preprint arXiv:2301.05386},
year = {2023}
}
Comments
Accepted for publication in Indian Journal of Pure and Applied Mathematics