A new bound for the 2/3 conjecture
  We show that any n-vertex complete graph with edges colored with three colors contains a set of at most four vertices such that the number of the neighbors of these vertices in one of the colors is at least 2n/3. The previous best value, proved by Erdos, Faudree, Gould, Gy\'arf\'as, Rousseau and Schelp in 1989, is 22. It is conjectured that three vertices suffice. 
Daniel Kr\'al' (DIMAP), Chun-Hung Liu, Jean-S\'ebastien Sereni   (LORIA), Peter Whalen, Zelealem Yilma (LIAFA)
cs.DM math.CO