Chain Dominated Orders

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. Key words: convex set, covering relation, dimension, digraph, interval order, jump number, partially ordered set, transitive reduction, truncated lattice, visibility relation.

• Type: Journal
• Year: 2006
• Where: ORDER
• Authors: Glen-Brug Guenver, Jimmy Leblet, Jean-Xavier Rampon
• Keywords: Chain, Interval Orders, ORDER 2006, Partial Orders