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Claim. For integers $b>a\ge1$ with $b\equiv\pm1\pmod a$ the rational $\alpha=2-\frac ab$ is a Turán exponent (Theorem 1.4), which subsumes the families $1+1/m$, $2-1/m$ and $2-2/m$ known before it; Corollary 1.5 deduces that every $2-1/m$ is a limit point of the Turán exponents. The paper also proposes a conjecture on $1$-subdivisions of bipartite graphs and shows that it implies the full statement of Problem 571; that implication is not a claim. The statements are recorded on the library's source card.

Covers. The instances $\alpha=2-\frac ab$ with $b>a\ge1$ and $b\equiv\pm1\pmod a$, each realized by a single bipartite graph. The statement for every rational $\alpha\in[1,2)$ is settled by the accepted claim page Adamczewski 2026.

Depends on. Nothing in this wiki; the result is the paper's own theorem.

Acceptance. Refereed: D. Y. Kang, J. Kim and H. Liu, On the rational Turán exponents conjecture, J. Combin. Theory Ser. B 148 (2021), 149--172, doi:10.1016/j.jctb.2020.12.003, a refereed journal. First posting: arXiv:1811.06916, v1 16 November 2018 (the date this page is named by). No reviewed evidence is listed: the site's commentary lists these exponents among the Turán exponents known before 2026 and credits the paper, but its label credits GPT-6 Astra with the full proof and is not an acceptance of this result.

Read depth. The statements are taken from the paper's abstract and the result list on the library card; no proof was read, and nothing is independently reviewed in this corpus.