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Claim. Theorem 10 (p. 4) of L. Boza, Exact values and bounds for Ramsey numbers of $C_4$ versus a star graph, arXiv:2409.12770v2, states, with $f(n)=R(C_4,K_{1,n})$ the function of Problem 552,

$$f(27)=33,\ f(28)=35,\ f(29)=36,\ f(30)=37,\ f(31)=38,\ f(32)=39,\ f(33)=40,\ f(37)=44,\ f(67)=76.$$

The abstract says this determines the eight previously unknown values of $f(n)$ for $n\le38$, so that with the values collected in the paper's tables (pp. 3--4) $f(n)$ is known for every $n\le38$. The lower bounds come from seven graphs of the House of Graphs database whose properties were verified by computer (Lemma 9), the upper bounds from the paper's inequalities relating different values of $f$. Remark 12 (p. 4) records $f(n)\ge n+\lceil\sqrt n\rceil$ for $2\le n\le82$ and $f(n)\ge f(n-1)+1$ for $3\le n\le39$, with no counterexample known for larger $n$. The statement is recorded on the result page Theorem 10 of the library home boza_2024_exact_values_bounds_ramsey_numbers_c4.

Covers. The value of $f(n)$ at $n=27,\dots,33$, $37$ and $67$, which completes the determination of $f(n)$ for every $n\le38$ together with the earlier values the paper tabulates. The value at every other $n$, and the second question, whether $f(n)\le n+\sqrt n-c$ for infinitely many $n$, are not settled by it.

Depends on. Nothing in this wiki; the lower bounds rest on the computer checks of Lemma 9, which this corpus has not rerun.

Standing. Claimed: the paper is an arXiv preprint, first posted on 19 September 2024, the date this page is named by, with version 2 of 12 June 2026 the text cited; no journal record was found on 2026-09-17.