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Claim. Let $f(n,k)$ be the least number such that in every two-coloring of the edges of $K_n$ one can find vertex-disjoint monochromatic copies of $K_k$, of either color, leaving at most $f(n,k)$ vertices uncovered. Theorem 6 of Burr, Erdős and Spencer (Trans. Amer. Math. Soc. 209 (1975), p. 94) states that for fixed $k$ and all sufficiently large $n$

$$f(n,k)=r(k,k-1)-1+\mathrm{rem}(n-r(k,k-1)+1,\,k),$$

where $r(k,k-1)$ is the off-diagonal Ramsey number and $\mathrm{rem}(a,b)$ the remainder of $a$ on division by $b$. So $f(n,k)$ is eventually periodic in $n$ with period $k$, between $r(k,k-1)-1$ and $r(k,k-1)+k-2$. The lower bound is a coloring with a set $B$ of $r(k,k-1)-1$ vertices colored with no red $K_k$ and no blue $K_{k-1}$, blue edges from $B$ to the rest and red edges inside the rest, so that no vertex of $B$ lies in a monochromatic $K_k$; the upper bound finds a large monochromatic clique by Ramsey's theorem, for $n\ge r(u,u)$ with $u=(k-1)(r(k,k)-r(k,k-1))+(k-1)(k-2)+1$, and uses it to complete leftover blue $K_{k-1}$'s to monochromatic $K_k$'s. This is the estimate Problem 1015 asks for, read, as the site's commentary reads it, with $n$ large in terms of $t=k$: the site's $f(t)$ is the eventual value of $f(n,t)$, and the exact growth of $f$ is that of $r(k,k-1)$.

Scope. Full, in the sense of the site's SOLVED label, which attaches to this determination. The two closing questions, whether $f(t)^{1/t}\to1$ and whether $f(t)\ll t$, are not stated in the paper; both have answer no because $r(k,k-1)\ge R(k-1)$ grows exponentially by Erdős's 1947 bound, a one-line consequence the problem page writes out and names as its own, which warrants nothing here. The site's printed formula, $f(t)=R(t,t-1)+x(t,n)$ with the same remainder $x$, exceeds the paper's by $1$; the problem page records the discrepancy against Moon's values for $k=3$ and does not repair it.

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

Acceptance. Reviewed: the site's curator, T. F. Bloom, labels the problem SOLVED and in its commentary credits Burr, Erdős and Spencer with the determination of $f$ for $n$ large in terms of $t$; the curator is independent of the authors. Refereed: the paper appeared in Transactions of the American Mathematical Society 209 (1975), 87--99, received 14 January 1974 (Crossref record; the record gives the year only, so the page's month and day are placeholders). The site's discussion thread and proof-claim tab are empty. OpenAlex lists 88 citing works (2026-09-18), whose titles record no dispute.

Read depth. The text read is the Rényi archive's scan, which the library does not hold: the opening of Section 5, the trivial bound, Theorem 6 and the lower-bound coloring were checked clause by clause and the upper-bound argument read for structure. Nothing here is independent review.