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A poset $P = (X,\prec)$ is a unit OC interval order if there exists arepresentation that assigns an open or closed real interval $I(x)$ of unitlength to each $x \in P$ so that $x \prec y$ in $P$ precisely when each pointof $I(x)$ is less than each point in $I(y)$. In this paper we give a forbiddenposet characterization of the class of unit OC interval orders and an efficientalgorithm for recognizing the class. The algorithm takes a poset $P $ as inputand either produces a representation or returns a forbidden poset induced in$P$.

Unit Interval Orders of Open and Closed Intervals