Beschreibung:
<jats:p>Barbour [l] invented an ingenious method of establishing the asymptotic distribution of the number <jats:italic>X</jats:italic> of specified subgraphs of a random graph. The novelty of his method relies on using the first two moments of <jats:italic>X</jats:italic> only, despite the traditional method of moments that involves all moments of <jats:italic>X</jats:italic> (compare [<jats:bold>8, 10, 11, 14</jats:bold>]). He also adjusted that new method for counting isolated trees of a given size in a random graph. (For further applications of Barbour's method see [<jats:bold>4</jats:bold>] and [<jats:bold>10</jats:bold>].) The main goal of this paper is to show how this method can be extended to a general setting that enables us to derive asymptotic distributions of subsets of vertices of a random graph with various properties.</jats:p>