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Claim. Janzer and Yip's Theorem 1.4 (p. 2 of both the arXiv version 1 and the published edition): every $n$-coloring of the edges of $K_{2^n+1}$ has a monochromatic odd cycle of length $O(n^{3/2}2^{n/2})$. In the notation of Problem 609, $f(n)=O(n^{3/2}2^{n/2})$, an exponential improvement on the trivial bound $2^n+1$ and on Girão and Hunter's $(2^n+1)/n^{1-\varepsilon}$. It is the case $\delta=2^{-n}$ of the paper's Theorem 1.5: if $0<\delta\le1$ and $N=(1+\delta)2^n$ is an integer, every $n$-coloring of $K_N$ has a monochromatic odd cycle of length at most $4n^{3/2}\delta^{-1/2}$. The proof builds a graph parameter that is submultiplicative under unions of color classes, equals $N$ on $K_N$ and is close to $2$ on graphs without short odd cycles, using the Lovász theta function and approximation theory. The paper is O. Janzer and F. Yip, Short monochromatic odd cycles, Math. Proc. Cambridge Philos. Soc. 181 (2026), no. 1, 781--788, DOI 10.1017/S0305004125101801, the site's [JaYi25]; its arXiv version is dated 17 June 2025, the date this page carries, and the publisher's record gives online publication on 27 March 2026. It is paged on the library's source card.

Covers. The upper bound $f(n)=O(n^{3/2}2^{n/2})$. Not covered: the growth order of $f(n)$, since the best lower bound, Day and Johnson's $2^{\sqrt{2\log_2n}-O(1)}$, is far smaller.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper appeared in the Mathematical Proceedings of the Cambridge Philosophical Society, volume 181. The site labels the problem OPEN, so its commentary crediting Janzer and Yip is not an acceptance, and no reviewed evidence is listed.

Read depth. The statements of Theorems 1.4 and 1.5 are checked in both editions; the proof was not reconstructed.