Entanglement of Formation is Non-monotonic with Concurrence-A Simple   Proof
  In this paper we explore the non-monotonic nature of entanglement of formation with respect to concurrence for pure bipartite states. For pure bipartite system, one of the basic physical reason of this non-monotonicity character is due to the existence of incomparable states, i.e., the pure bipartite states which are not convertible to each other by LOCC with certainty. 
Indrani Chattopadhyay, Debasis Sarkar