Unit Interval Orders of Open and Closed Intervals

Alan Shuchat
Randy Shull
Ann N. Trenk

Abstract

A poset P = (X [symbol]) is a unit OC interval order if there exists a representation that assigns an open or closed real interval I(x) of unit length to each x [symbol] P so that x [symbol] y in P precisely when each point of I(x) is less than each point in I(y). In this paper we give a forbidden poset characterization of the class of unit OC interval orders and an efficient algorithm for recognizing the class. The algorithm takes a poset P as input and either produces a representation or returns a forbidden poset induced in P.