The length, the width and the cutset-number of finite ordered sets (Q1068861)

A cutset F(x) for an element x of a finite poset P is a set of elements of P, incomparable to x, such that F(x)\(\cup x\) meets every maximal chain of P. The authors study posets P with the property: for every x, card F(x)\(<3\); they show that width of \(P\leq length\) of P \(+3\). The proof introduces a new concept, that of a simple finite poset: its number of maximal chains is equal to its width.