The isoperimetric number of random regular graphs
European Journal of Combinatorics
Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
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
Theoretical Computer Science
Random regular graphs with edge faults: expansion through cores
Theoretical 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
Graphs, Hypergraphs and Hashing
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
Routing on butterfly networks with random faults
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Expansion properties of a random regular graph after random vertex deletions
European Journal of Combinatorics
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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 of other edges with a given fault probability? We improve previous results on this problem in two respects: First, expansion properties are preserved for much higher fault probabilities than known before. Second, our results apply to random regular graphs of any degree which is at least 4. Previous results apply only to degrees of at least 42. Moreover, the techniques used by us are more elementary than those used in previous work in this area.