\magnification=1200
\hsize=4in
\nopagenumbers
\noindent
%
%
{\bf Ben Wieland and Anant P. Godbole}
%
%
\medskip
\noindent
%
%
{\bf On the Domination Number of a Random Graph}
%
%
\vskip 5mm
\noindent
%
%
%
%
In this paper, we show that the domination number 
$D$ of a random graph enjoys as sharp a concentration as does its chromatic number
 $\chi$.  We first prove this fact for the sequence of graphs 
$\{G(n,p_n\},\; n\to\infty$, where a {\it two point concentration}
is obtained with high probability for $p_n=p$ (fixed) or for a 
sequence $p_n$ that approaches zero sufficiently slowly.  We then
consider the infinite graph $G({\bf Z}^+, p)$, where $p$ is fixed, 
and prove a {\it three} point concentration for the domination 
number with probability one. The main results are 
proved using the second moment method together with the Borel Cantelli lemma.


\bye

.
