3-star factors in random -regular graphs

The small subgraph conditioning method first appeared when Robinson and the second author showed the almost sure hamiltonicity of random d -regular graphs. Since then it has been used to study the almost sure existence of, and the asymptotic distribution of, regular spanning subgraphs of various types in random d -regular graphs and hypergraphs. In this paper, we use the method to prove the almost sure existence of 3-star factors in random d -regular graphs. This is essentially the first application of the method to non-regular subgraphs in such graphs.