منابع مشابه
Cycle length distributions in random permutations with diverging cycle weights
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متن کاملAn Improved Upper Bound on the Length of the Longest Cycle of a Supercritical Random Graph
We improve Luczak’s upper bounds on the length of the longest cycle in the random graph G(n,M) in the “supercritical phase” where M = n/2 + s and s = o(n) but n2/3 = o(s). The new upper bound is (6.958 + o(1))s2/n with probability 1 − o(1) as n → ∞. Letting c = 1+2s/n, the equivalence between G(n, p) and G(n,M) implies the same result for G(n, p) where p = c/n, c → 1, c − 1 = ω(n−1/3).
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1968
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1968-0228032-3