  We consider random graphs in which the edges are allowed to be dependent. In
our model the edge dependence is quite general, we call it $p$-robust random
graph. It means that every edge is present with probability at least $p$,
regardless of the presence/absence of other edges. This is more general than
independent edges with probability $p$, as we illustrate with examples. Our
main result is that for any monotone graph property, the $p$-robust random
graph has at least as high probability to have the property as an Erdos-Renyi
random graph with edge probability $p$. This is very useful, as it allows the
adaptation of many results from classical Erdos-Renyi random graphs to a
non-independent setting, as lower bounds.
