(1) FST de l’Université de Nantes, 2, rue de la Houssinière, BP 92208, F-44322 Nantes Cedex 3, France;(2) Université d’Orléans, L.I.F.O., Bat IIIA, Rue Léonard de Vinci, B.P. 6759, F-45067 Orléans Cedex 2, France
Abstract:
We study finite partial orders which have a chain such that every element of the order either belongs to this chain or has all its covers in this chain. We show that such orders are exactly the orders being both interval orders and truncated lattices. We prove that their jump number is polynomially tractable and that their dimension is unbounded. We also show that every order admits a visibility model having such an order as host.