3-star factors in random d-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 nonregular subgraphs in such graphs.

• Type: Journal
• Year: 2006
• Where: EJC
• Authors: Hilda Assiyatun, Nicholas C. Wormald
• Keywords: EJC 2006, EJC 2007, Random D-regular Graphs, Subgraph Conditioning Method, Sure Existence