In the wikipedia article on the probabilistic method mentions in the paragraph "First Example" a proof attributed to Erdős. It is attributed to him in a 1947 paper. There is no 1947 paper in the references, neither is it mentioned in the talk.
Where can I find this paper (title? download link?)
Related Question that doesn't mention the paper either.
He wrote a lot of papers in 1947, and I can't find a matching one by title alone.
It's in Some Remarks on the Theory of Graphs, available here (bad scan) or here if you have access. Theorem I contains the result that $f(k, k) > 2^{k/2}$, which is what the example in the wiki article is about. I think the proof in the paper is the one in the footnote (a) of the wiki article.