domains, the nucleotide binding domains (NBDs), but which have evolved to couple the energy released by binding and hydrolysis of ATP to processes other than transbilayer transport. These include proteins involved in chromatin organization (13), DNA repair, telomere maintenance (15, 44), and mRNA trafficking through the nuclear pore (23). The molecular mechanism described below for ATP catalysi...

Erdős and Hajnal conjectured that for every graph H there is a constant ε = ε(H) > 0 such that every graph G that does not have H as an induced subgraph contains a clique or a stable set of order Ω(|V (G)|ε). The conjecture would be false if we set ε = 1; however, in an asymptotic setting, we obtain this strengthened form of Erdős and Hajnal’s conjecture for almost every graph H, and in particu...