The isoperimetric number of random regular graphs
European Journal of Combinatorics
On the fault tolerance of the butterfly
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
Bounds to the throughput of an interconnection network
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
The Giant Component Threshold for Random Regular Graphs with Edge Faults
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Short Vertex Disjoint Paths and Multiconnectivity in Random Graphs: Reliable Network Computing
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
On the Fault Tolerance of Fat-Trees
Euro-Par '97 Proceedings of the Third International Euro-Par Conference on Parallel Processing
On the fault tolerance of some popular bounded-degree networks
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Efficient self-embedding of butterfly networks with random faults
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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Let G be a given graph (modeling a communication network) which we assume suffers 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 robustness 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, fixed and p = κ/d, κ ≥ 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.