---

Claim. The Theorem (p. 259) of J. W. Moon, Disjoint triangles in chromatic graphs, Math. Mag. 39 (1966), no. 5, 259--261. Write $\mu(G_n)$ for the largest number of vertex-disjoint monochromatic triangles in a two-coloring $G_n$ of the edges of $K_n$. Then $[\tfrac13n]-1\le\mu(G_n)\le[\tfrac13n]$ for every $G_n$, and $\mu(G_n)=[\tfrac13n]$ when $n\equiv2\pmod3$ and $n\ge8$. The closing remark (p. 261) says that the lower bound is attained whenever $n\ge3$ and the second part does not apply, and prints no example. In the leftover count of Problem 1015, where $f(n,3)$ is the maximum of $n-3\mu(G_n)$, this gives $f(n,3)\le4$ for every $n$ other than $5$ (at most $3$ for $n\equiv0$ and $4$ for $n\equiv1\pmod3$ by the first part, and $2$ for $n\equiv2\pmod3$, $n\ge8$, by the second), and $f(n,3)=2$ for $n\equiv2\pmod3$, $n\ge8$. Math. Mag. 39, no. 5, is the November--December issue, so the page's day is a placeholder.

Covers. The case $t=3$, $f(3)=4$, the site's value. The upper bound is Moon's theorem. Moon leaves to the reader the colorings that attain $4$ for $n\equiv1\pmod3$; the $k=3$ case of the Figure 6 coloring of Burr, Erdős and Spencer (1975), their claim page, supplies them. Nothing for $t\ge4$ or for the two closing questions.

Depends on. Nothing in this wiki; the theorem rests on the paper's own case analysis of $K_8$ and the fact that every two-coloring of $K_6$ has a monochromatic triangle.

Acceptance. Refereed journal publication in Mathematics Magazine 39 (1966), no. 5, 259--261, which is the refereed evidence. The site's label SOLVED rests on Burr, Erdős and Spencer, so the curator's credit of $f(3)=4$ to Moon is not listed as reviewed. The proof (pp. 259--261) is followed on the library's result page, with the claims about its Figures 2--4 taken as printed; nothing here is independently reviewed.