The order-interval hypergraph of a finite poset and the König property Original Research Article

We study the hypergraph H(P) whose vertices are the points of a finite poset and whose edges are the maximal intervals in P (i.e. sets of the form I = {{v ϵ P: p ⩽ ν ⩽ q}}, p minimal, q maximal). We mention resp. show that the problems of the determination of the independence number α, the point covering number τ, the matching number v and the edge covering number p are NP-complete. For interval orders we describe polynomial algorithms and prove the König property (v = τ) and the dual König property (a = p). Finally we show that the (dual) König property is preserved by product.