NP hard relation with NP complete If any problem P is NP complete then if there is a polynomial time reduction of P to another problem R then what can we say about R.Is it NP-hard or NP complete ?
From Theory of computation of Hopcroft,Ullman theorem 10.4 it says it would be NP complete but there some times when i see that it is NP-Hard in some other reference . is there any condition when it is NP Hard or NP Complete .Or i misunderstood the theorem .
NP-hard means that all the problems in NP reduces to this.  NP-complete means that it is in NP as well.

Sometimes we say a problem is NP-hard when it is obviously NP-complete.  But this is because we want to stress the hardness of the problem, and also that it should be trivial that the problem is in NP.