A Study on the Amount of Random Graph Groupies
Daodi Lu · arXiv (Cornell University) · 2013
In 1980, Ajtai, Komlos and Szemer{é}di defined "groupie": Let $G=(V,E)$ be a simple graph, $|V|=n$, $|E|=e$. For a vertex $v\in V$, let $r(v)$ denote the sum of the degrees of the vertices adjacent to $v$. We say $v\in V$ is a {\it groupie}, if $\frac{r(v)}{°(v)}\geq\frac{e}{n}.$ In this paper, we prove that in random graph $B(n,p)$, $0