Subcritical component bound for a binomial random graph
= Subcritical component bound for a binomial random graph
For every fixed $\varepsilon>0$, every <connected component of a graph>[component] of $G(n,(1-\varepsilon)/n)$ has $O_\varepsilon(\log n)$ vertices <with high probability>. A breadth-first exploration is dominated by a branching process of mean $1-\varepsilon$; its total progeny has an exponentially decreasing tail.