A simple proof characterizing interval orders with interval lengths between 1 and k
Simona Boyadzhiyska, Garth Isaak, Ann N. Trenk · Involve a Journal of Mathematics · 2018
A poset P = (X, ≺) has an interval representation if each x ∈ X can be assigned a real interval I x so that x ≺ y in P if and only if I x lies completely to the left of I y .Such orders are called interval orders.Fishburn (1983Fishburn ( , 1985) ) proved that for any positive integer k, an interval order has a representation in which all interval lengths are between 1 and k if and only if the order does not contain (k+2)+1 as an induced poset.In this paper, we give a simple proof of this result using a digraph model.