On Certain Spanning Subgraphs of Random Graphs

An improvement of Riordan’s result on the threshold probability of the occurrence of a spanning subgraph in a random graph is obtained for some classes of subgraphs. In particular, this result implies an improved bound for the maximum power of a Hamiltonian cycle in a random graph. Moreover, a sharp asymptotic threshold probability for a random graph to contain spanning subgraphs from a wide class of $$k$$ -degenerate graphs is found.