Analysis of edge deletion processes on faulty random regular graphs

Abstract

Random regular graphs are, at least theoretically, popular communication networks. The reason for this is that they combine low (that is constant) degree with good expansion properties crucial for efficient communication and load balancing. When any kind of communication network gets large one is faced with the question of fault tolerance of this network. Here we consider the question: Are the expansion properties of random regular graphs preserved when each edge gets faulty independently with a given fault probability? We improve previous results on this problem: Expansion properties are shown to be preserved for much higher fault probabilities and lower degrees than was known before. Our proofs are much simpler than related proofs in this area. © Springer-Verlag Berlin Heidelberg 2000.