Random regular graphs of high degree

Random d‐regular graphs have been well studied when d is fixed and the number of vertices goes to infinity. We obtain results on many of the properties of a random d‐regular graph when d=d(n) grows more quickly than . These properties include connectivity, hamiltonicity, independent set size, chromatic number, choice number, and the size of the second eigenvalue, among others. ©2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 346–363, 2001.