Proves robust percolation and hyperstability extensions of the Erdős-Gallai theorem guaranteeing long cycles in graphs of given average degree.
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A hybrid static-dynamic analysis yields precise asymptotics for small components and extremely sharp bounds on the largest non-giant component in the Bohman-Frieze process near the critical point.
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Robustness and hyperstability for the Erd\H{o}s-Gallai theorem
Proves robust percolation and hyperstability extensions of the Erdős-Gallai theorem guaranteeing long cycles in graphs of given average degree.
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Counting subgraphs in bounded-size Achlioptas processes
A hybrid static-dynamic analysis yields precise asymptotics for small components and extremely sharp bounds on the largest non-giant component in the Bohman-Frieze process near the critical point.