Unit Mixed Interval Graphs
  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, however our approach provides an algorithm that produces such a representation, as well as a forbidden graph characterization. 
Alan Shuchat, Randy Shull, Ann N. Trenk, Lee C. West
math.CO