Corrigendum to "Counting connected graphs inside-out" [J. Combin. Theory Ser. B 93 (2005) 127-172]
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C (1) 2 (n,m) C2(n,m) = (1 − O(r−1))P(Xn = 0).) We have realized that our proof covers only m = O(n). We show in this corrigendum how to modify the proof to cover the full range m = O(n lnn). We assume familiarity with Section 6 of [3], and the main results in [2]. Equation numbers of the form (a.b) refer to [3], and those of the form (a) refer to [2]. First of all, by Theorem 1 in [1], C2(n,m), the total number of 2-cores, is asymptotic to (2m − 1)!! √ nvarY f (λ) λ2m exp (−E[S] − E2[S]), S := 1 4m n ∑
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[2] Nicholas C. Wormald,et al. Asymptotic enumeration of sparse graphs with a minimum degree constraint , 2003, J. Comb. Theory A.
[3] Nicholas C. Wormald,et al. Counting connected graphs inside-out , 2005, J. Comb. Theory, Ser. B.