Ramsey Numbers of Books and Quasirandomness

The book graph $$B_n^{(k)}$$ consists of n copies Kk+1 joined along a common Kk. Ramsey numbers are known to have strong connections the classical cliques. Recently, first author determined asymptotic order these for fixed k, thus answering an old question Erdős, Faudree, Rousseau, and Schelp. In this paper, we provide simpler proof theorem. Next, author, present different that avoids use Szemerédi’s regularity lemma, providing much tighter control on error term. Finally, prove conjecture Nikiforov, Schelp by showing all extremal colorings problem quasirandom.