We study the asymptotic behavior of the independence number of a random subgraph of a certain (r, s)-distance graph. We provide upper and lower bounds for the critical edge survival probability under which a phase transition occurs, i.e., large new independent sets appear in the subgraph, which did not exist in the original graph.

中文翻译：

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一定距离图的独立数的稳定性

我们研究某个（r，  s）距离图的随机子图的独立性的渐近行为。我们提供临界边缘生存概率的上限和下限，在该概率下发生相变，即子图中出现了新的独立的大集合，而原始图中不存在新的独立集合。