Unit Interval Orders of Open and Closed Intervals

Abstract

A poset $P=(X,\prec )$ 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 $x\in P$ so that $x\prec y$ 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 $P$.

18 pages, 5 figures

References in corpus (1)

• Unit Mixed Interval Graphs