  A linear-interval order is the intersection of a linear order and an interval
order. For this class of orders, several structural results have been known.
This paper introduces a new subclass of linear-interval orders. We call a
partial order a \emph{linear-semiorder} if it is the intersection of a linear
order and a semiorder. We show a characterization and a polynomial-time
recognition algorithm for linear-semiorders. We also prove that being a
linear-semiorder is a comparability invariant, showing that incomparability
graphs of linear-semiorders can be recognized in polynomial time.
