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Claim. For $k\in\{3,4\}$ and every $s\ge2$ the rational $\alpha=1+\frac1k-\frac1{sk}$, that is, $\frac43-\frac1{3s}$ and $\frac54-\frac1{4s}$, is a Turán exponent. Writing $K^k_{s,t}$ for the graph obtained from $K_{s,t}$ by replacing each edge with a path of length $k$, Theorem 1.2 proves $\mathrm{ex}(n,K^k_{s,t})=O(n^{1+1/k-1/(sk)})$ for $k\in\{3,4\}$ and all $s,t\ge2$, the cases $k=3,4$ of a conjecture of Conlon, Janzer and Lee; the matching lower bound, for t large in terms of s and k, is Bukh and Conlon's random algebraic construction. The statements are recorded on the library's source card.

Covers. The instances $\alpha=\frac43-\frac1{3s}$ and $\alpha=\frac54-\frac1{4s}$ for $s\ge2$, 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: T. Jiang and Y. Qiu, Turán numbers of bipartite subdivisions, SIAM J. Discrete Math. 34 (2020), no. 1, 556--570, doi:10.1137/19M1265442, a refereed journal. First posting: arXiv:1905.08994, v1 22 May 2019 (the date this page is named by), v2 31 May 2019. 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.