Almost all Cayley graphs have diameter 2
Discrete Mathematics
Random regular graphs of high degree
Random Structures & Algorithms
Random Regular Graphs of Non-Constant Degree: Connectivity and Hamiltonicity
Combinatorics, Probability and Computing
Expansion properties of random Cayley graphs and vertex transitive graphs via matrix martingales
Random Structures & Algorithms
Sparse pseudo-random graphs are Hamiltonian
Journal of Graph Theory
Random Cayley graphs and expanders
Random Structures & Algorithms
Repeated communication and Ramsey graphs
IEEE Transactions on Information Theory
The chromatic number of random Cayley graphs
European Journal of Combinatorics
The range of thresholds for diameter 2 in random Cayley graphs
European Journal of Combinatorics
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In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and several similarities and differences are pointed out. For many properties our results for the general case are as strong as the known results for random Cayley graphs and sometimes improve the previously best results for the Cayley case. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011, © 2012 Wiley Periodicals, Inc. (Supported by The Royal Physiographic Society in Lund.)