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Robustness and hyperstability for the Erd\H{o}s-Gallai theorem

math.CO · 2026-07-02 · conditional · novelty 8.0

Randomly keeping each edge with probability about 1/d still leaves a cycle of length nearly d in any average-degree-d graph, and graphs with no d-cycle are nearly disjoint unions of components with small vertex covers.

Counting subgraphs in bounded-size Achlioptas processes

math.PR · 2026-05-10 · unverdicted · novelty 7.0

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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  • Counting subgraphs in bounded-size Achlioptas processes math.PR · 2026-05-10 · unverdicted · none · ref 11

    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.