Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claims
2018_06_07_jiang_ma_yepremyan: Jiang, Ma and Yepremyan (Combin. Probab. Comput. 2022): for every s at least 2 the rational 2 minus 2/(2s+1), and also 7/5, is the Turán exponent of a single bipartite graph; infinitely many instances of Problem 571.
2018_11_16_kang_kim_liu: Kang, Kim and Liu (J. Combin. Theory Ser. B 2021): 2 minus a/b is a Turán exponent for all integers b > a at least 1 with b congruent to plus or minus 1 modulo a; infinitely many instances of Problem 571.
2019_03_25_conlon_janzer_lee: Conlon, Janzer and Lee (Combinatorica 2021): the 1-subdivision of K_{s,t} has Turán exponent 3/2 minus 1/(2s) for t large in terms of s, and a graph with exponent 1 + s/(sk+1) exists for all s, k; infinitely many instances.
2019_05_22_jiang_qiu: Jiang and Qiu (SIAM J. Discrete Math. 2020): the k-subdivisions of K_{s,t} have Turán exponent 1 + 1/k minus 1/(sk) for k = 3 and k = 4 and all s at least 2; infinitely many instances of Problem 571.
2019_08_06_jiang_qiu: Jiang and Qiu (Combin. Probab. Comput. 2023): 1 + p/q is a Turán exponent for all positive integers q > p squared, from unevenly subdivided complete bipartite graphs; infinitely many instances of Problem 571.
2020_07_06_jiang_jiang_ma: Jiang, Jiang and Ma (Ann. Appl. Math. 2022): 2 minus a/b is a Turán exponent whenever the floor of b/a cubed is at most a and a is at most b/(floor(b/a)+1) plus 1; infinitely many instances of Problem 571.
2022_03_07_conlon_janzer: Conlon and Janzer (Adv. Comb. 2022): every rational 2 minus a/b with b at least the larger of a and (a-1) squared is a Turán exponent, by the Bukh–Conlon upper bound for the rooted trees of Jiang, Jiang and Ma.
2026_07_21_jiang_longbrake_yepremyan: A 2026 preprint of Jiang, Longbrake and Yepremyan: 1 + (rt-1)/(2rt+2r) is a Turán exponent for t at least 2 and r at least 2t+3, by bounding rooted powers of the subdivided height-two tree; infinitely many instances.
2026_09_03_adamczewski: A Lean proof, found by GPT-6 Astra and published in Adamczewski's repository, that every rational alpha in [1,2) is the Turán exponent of a finite bipartite graph; accepted on Lean built here.