Claims

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1980_01_01_komlos_sulyok_szemeredi: Correct, but answers the supercritical case the site's label credits (edge probability lambda/n with lambda > 1), not the Statement (edge probability 1/n), so it does not count toward the problem's standing. Komlós, Sulyok and Szemerédi bound the second largest component by O(log n) there.

1997_04_01_aldous: Aldous (Ann. Probab. 25 (1997)) proves that the ordered component sizes of G(n, 1/n + t n^(-4/3)), scaled by n^(-2/3), converge to Brownian excursion lengths; at t = 0 the second largest component has order n^(2/3); refereed.

2026_08_25_alexeev: Boris Alexeev's Lean development gives the second largest component of G(n, λ/n) order n^(2/3) at λ = 1, the problem's parameter, and logarithmic order with an explicit coefficient for every fixed λ ≠ 1; unbuilt by this corpus.

2026_10_04_ding: Jingxuan Ding's Lean development describes the second largest component of the uniform random graph G(n, M) in five sparse regimes: order n^(2/3) in the critical window, logarithmic order away from it; unbuilt by this corpus.

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