Computer Science, Mathematics
A poset P=(V,≺) 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 ∈ P so that x ≺ 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.
Shuchat, A., Shull, R., & Trenk, A. N. (2015). Unit Interval Orders of Open and Closed Intervals. Order. DOI 10.1007/s11083-015-9354-z