# Lower bound for diagonal Ramsey numbers —- reference request

Using the first moment method, in 1947 Erd\H{o}s gave a lower bound on the diagonal Ramsey numbers $$R(k,k)$$: $$R(k,k) \geq (1+o(1))\frac{k}{e\sqrt{2}} 2^{k/2}.$$ In 1975 Spenser used the Lov\’asz Local Lemma to improve this by a factor of $$2$$, to $$(1+o(1))(k\sqrt{2}/e)2^{k/2}$$.

In between these two lower bounds, there is the one you get via the alteration or deletion method: $$R(k,k) \geq (1+o(1))\frac{k}{e} 2^{k/2}.$$

I’m trying to discover who first noticed this last bound, and when? Was it before or after Spencer’s improvement? I’ve seen the bound in numerous sets of notes online (and learned it as a graduate student), but with no attribution. Maybe it’s just folklore’’.

(I’m leading a summer reading group in Ramsey Theory, and I plan on Tuesday to tell them the history of upper and lower bounds on diagonal Ramsey numbers.)

Though we do not know of an explicit reference, a simple application of the deletion method which improves Erdos' bound by a factor of $$\sqrt{2}$$ was surely known before Spencer's work.