Distribution of the number of spanning regular subgraphs in random graphs

In this paper, we examine the moments of the number of d ‐factors in \documentclass{article}\usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}\mathcal{ G}(n,p)\end{align*} \end{document} for all p and d satisfying d 3 = o ( p 2 n ). We also determine the limiting distribution of the number of d ‐factors inside this range with further restriction that \documentclass{article}\usepackage{mathrsfs, amsmath, amssymb}\pagestyle{empty}\begin{document}\begin{align*}(1-p)\sqrt{dn}\to\infty\end{align*} \end{document} as n → ∞ .© 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013