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Claim. Write $H$ for the complement of an $n$-vertex graph $G$. Every $k+2$ vertices of $G$ induce a subgraph of maximum degree at least $k$ exactly when every $k+2$ vertices of $H$ induce a subgraph of minimum degree at most $1$, so $f(n,k)$ of Problem 614 is $\binom n2$ minus the largest number of edges of an $n$-vertex graph with that property. The note draws three consequences. For $k=1$ the property says that $H$ is triangle-free, so by Mantel's theorem

$$f(n,1)=\binom n2-\left\lfloor\frac{n^2}4\right\rfloor\qquad(n\ge2)$$

(its Theorem 2.1). For $k=2$ the admissible $H$ are exactly the $C_4$-free graphs, since a $4$-vertex graph of minimum degree at least $2$ is Hamiltonian, so $f(n,2)=\binom n2-\mathrm{ex}(n,C_4)$ for $n\ge4$ (Theorem 3.1). For each fixed $k\ge2$, with $\mathcal F_k^{\min}$ the finite family of graphs on $k+2$ vertices that have minimum degree at least $2$ and lose that property when any edge is deleted, the admissible $H$ are exactly the $\mathcal F_k^{\min}$-free graphs, so $f(n,k)=\binom n2-\mathrm{ex}(n,\mathcal F_k^{\min})$ (Theorem 4.5). An exhaustive computer search gives the families for $3\le k\le6$; for $k=3$ it is $\{C_5,K_{2,3},K_1\vee2K_2\}$, where $K_1\vee2K_2$ is a vertex joined to two disjoint edges, so $f(n,3)=\binom n2-\mathrm{ex}(n,{C_5,K_{2,3},K_1\vee 2K_2})$ for $n\ge5$ (Corollary 4.6).

Covers. The instance $k=1$, where $f(n,1)$ is determined for every $n\ge2$. For $k\ge2$ the result is a reduction: $f(n,k)$ equals $\binom n2$ minus a Turán number of a finite family, and the note asserts that identity as its answer, but the Turán numbers $\mathrm{ex}(n,C_4)$ and $\mathrm{ex}(n,\mathcal F_k^{\min})$ for $k\ge3$ are not determined there or elsewhere, so no value of $f(n,k)$ with $k\ge2$ is settled. The thread post says that the authors do not know whether this Turán-type reformulation is the kind of answer Erdős had in mind.

The posting. The note was posted on the site's discussion thread on 7 January 2026 by Quanyu Tang, who describes it as a short note written with a coauthor named only as Ma; it is hosted in a GitHub repository under Tang's name, linked above at the commit of that day, and carries no title, author list or date on its face. The determination of $f(n,1)$ is Mantel's theorem applied to the complement; the general reduction is a few lines of elementary graph theory, and the families for $3\le k\le6$ come from a computer search whose code the repository's description names but whose output is given only as figures.

Standing. The claim is claimed: the note is unrefereed and has no publication record, no response appears on the thread, the site's proof-claim tab for the problem is empty, the site labels the problem OPEN and the community database records it open and unformalized (as of 2026-10-07). The site's remarks do not mention the note. No independent review of the note is recorded.