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

Abstract

The partially ordered set P is an (α, β, γ) ordered set if the width of P≥α, the length of any chain of P≤β and the cut-set number ≤γ. We will prove that if P is an (α, β, γ) ordered set then P contains a ‘simple’ (α, β, γ) ordered set and use this result to prove that if P has the 3 cutset property, then width of P ≤ length of P+3.