Computer Science, Mathematics
In this paper we extend the work of Rautenbach and Szwarcfiter  by giving a structural characterization of graphs that can be represented by the intersection of unit intervals that may or may not contain their endpoints. A characterization was proved independently by Joos in , however our approach provides an algorithm that produces such a representation, as well as a forbidden graph characterization.
Shuchat, A., Shull, R., Trenk, A. N., & West, L. C. (2014). Unit Mixed Interval Graphs. Congressus Numerantium, 221: 189-223.