KOLMOGOROV BOUNDS FOR THE NORMAL APPROXIMATION OF THE NUMBER OF TRIANGLES IN THE ERD?S–RÉNYI RANDOM GRAPH

We bound the error for normal approximation of number triangles in Erd?s–Rényi random graph with respect to Kolmogorov metric. Our bounds match best available Wasserstein obtained by Barbour et al. [(1989). A central limit theorem decomposable variables applications graphs. Journal Combinatorial Theory, Series B 47: 125–145], resolving a long-standing open problem. The proofs are based on new variant Stein–Tikhomirov method—a combination Stein's method and characteristic functions introduced Tikhomirov [(1976). rate convergence weakly dependent variables. Vestnik Leningradskogo Universiteta 158–159, 166].