  We give a complete characterization of mixed unit interval graphs, the
intersection graphs of closed, open, and half-open unit intervals of the real
line. This is a proper superclass of the well known unit interval graphs. Our
result solves a problem posed by Dourado, Le, Protti, Rautenbach and
Szwarcfiter (Mixed unit interval graphs, Discrete Math. 312, 3357-3363 (2012)).
