Tidier examples for lower bounds on diagonal Ramsey numbers (Q1914003)

It is known that the diagonal Ramsey numbers \(R(k, k)\) are bounded below by \[ (1+ o(1)){\sqrt 2\over e} k2^{{k\over 2}}. \] In this note, the authors prove the existence of a ``nice'' family of graphs which demonstrate this bound. They prove Theorem 2: There exists a family \((H_k: k= 1, 2,\dots)\) of quasi-random, regular, self-complementary graphs such that (a) \(\alpha(H_k)= \omega(H_k)< k\), and (b) \(|V(H_k)|= (1+ o(1)){\sqrt 2\over e} k2^{{k\over 2}}\).