The star 2-process â€˜â€˜greedilyâ€™â€™ generates graphs with maximum degree 2 in a natural way. We can obtain information about the final graph of this process; for instance, that is almost surely 2-regular. We also find the probability of hamiltonicity and Poisson approximations of the distributions of numbers of cycles and short cycles. Q 1997 John Wiley Å½ . &â€¦ (More)

It is shown that for each r 3, a random r-regular graph on 2n vertices is equivalent in a certain sense to a set of r randomly chosen disjoint perfect matchings of the 2n vertices, as n ! 1. This equivalence of two sequences of probabilistic spaces, called contiguity, occurs when all events almost sure in one sequence of spaces are almost sure in the other,â€¦ (More)