3-star factors in random d-regular graphs

Authors:
Hilda Assiyatun;Nicholas Wormald
Affiliations:
Department of Mathematics, Institut Teknologi Bandung, Bandung, Indonesia and University of Melbourne;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada and Department of Mathematics and Statistics, University of Melbourne
Venue:
European Journal of Combinatorics - Special issue on extremal and probabilistic combinatorics
Year:
2006

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Abstract

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.