On a property of the $n$-dimensional cube
  We show that in any subset of the vertices of $n$-dimensional cube that contains at least $2^{n-1}+1$ vertices ($n\geq 4$), there are four vertices that induce a claw, or there are eight vertices that induce the cycle of length eight. 
Rafayel Kamalian, Arpine Khachatryan
cs.DM math.CO