The following theorem about the degree sequences of finite simple graphs is quite easy to prove from the Erdos-Gallai theorem.

Let $0 \lt \alpha \le \beta \lt n$ be integers. Call $(\alpha,\beta,n)$ *paragraphical* if every integer sequence $\alpha \le d_1,\ldots,d_n \le \beta$ with even sum is the degree sequence of a simple graph.
Then $(\alpha,\beta,n)$ is paragraphical **iff**
$$ n \ge \biggl\lfloor\frac{ (\alpha+\beta+1)^2 }{4 \alpha} \biggr\rfloor.$$

I find it really hard to believe that nobody published this anywhere, but can I find it? The question is: **where is it**?

Thanks!