On a Ramsey-type problem of Erd\H{o}s and Pach
  In this paper we show that there exists a constant $C>0$ such that for any graph $G$ on $Ck\ln k$ vertices either $G$ or its complement $\bar{G}$ has an induced subgraph on $k$ vertices with minimum degree at least $\frac12(k-1)$. This affirmatively answers a question of Erd\H{o}s and Pach from 1983. 
Ross J. Kang, Eoin Long, Viresh Patel, Guus Regts
math.CO