= Achlioptas process
{c}
{title2=$G_{m+1}=G_m\cup\{e_{m,\omega_m}\}$}
At each step offer a fixed number of independent uniform candidate <edges> on a fixed vertex set, and let a rule select one. The standard two-choice model offers two candidates. The rule may depend on the entire previously exposed history. Repeated already present <edges> make no change in the independent-candidate version; another usual version offers only absent <edges>. The <forced merging of large components> and <persistence of unsampled graph components> apply to both over a linear number of steps. Fixed choice is essential in the <continuity of fixed-choice percolation> argument.
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