  We consider the random right-angled Coxeter group whose presentation graph is
an Erdos-Renyi random graph on n vertices with edge probability p=p(n). We
establish that p=1/\sqrt{n} is a threshold for relative hyperbolicity of the
random right-angled Coxeter group . As a key step in the proof, we determine
the minimal number of pairs of generators that must commute in a right-angled
Coxeter group which is not relatively hyperbolic, a result which is of
independent interest.
