Abstract
Let P be a finite ordered set. One can easily show that w( P)-1 <= s( P) <= vertical bar P vertical bar-h( P), where s( P) is the jump number of P, w( P) is the width of P and h( P) is the height of P. The recognition problem of ordered sets for which w( P)-1 = s( P) "called Dilworth posets" is NP-complete. The purpose of this paper is to give an "effective" characterization of all ordered sets P for which s( P)=vertical bar P vertical bar-h(P).