Regular trees in random regular graphs
Eran Makover, Jeffrey McGowan · arXiv (Cornell University) · 2006
We investigate the size of the embedded regular tree rooted at a vertex in a $d$ regular random graph. We show that almost always, the radius of this tree will be ${1/2}\log n$, where $n$ is the number of vertices in the graph. And we give an asymptotic estimate for Gauss' Hypergeometric Function.