Random Regular Graphs with Edge Faults: Expansion through Cores

Let G be a given graph (modelling a communication network) which we assume suuers from static edge faults: That is we let each edge of G be present independently with probability p (or absent with fault probability f = 1 ? p). In particular we are interested in ro-bustness results for the case that the graph G itself is a random member of the class of all regular graphs with given degree d. Here we deal with expansion properties of faulty random regular graphs and show: For d 42, xed and p = =d ; 20, a random regular graph with fault probability f = 1 ? p contains a linear-sized subgraph which is an expander almost surely. This subgraph can be found by a simple linear-time algorithm.