Survival under random coverings of trees
Let \(v_ 1,...,v_ n\) be a random ordering of the nodes of a rooted tree \(T_ n\). If N(v) denotes the set of consisting of node v and all nodes joined to v, the nodes in \(N(v_ 1)\cup...\cup N(v_ j)\) are called ``j-covered'' and the remaining nodes ``j-survivors''. In the paper the expected number s(n,j) of j-survivors in the trees \(T_ n\) in some given family \({\mathcal F}\) of rooted trees is studied, as well as the expected value \(c_ r(n)\) of the least integer j such that the root r of \(T_ n\) is j-covered. The investigations are motivated by some problems arising in the context of security considerations for communication networks.
scientific article; zbMATH DE number 4055635