  We continue the study of linear layouts of graphs in relation to known data
structures. At a high level, given a data structure, the goal is to find a
linear order of the vertices of the graph and a partition of its edges into
pages, such that the edges in each page follow the restriction of the given
data structure in the underlying order. In this regard, the most notable
representatives are the stack and queue layouts, while there exists some work
also for deques.
  In this paper, we study linear layouts of graphs that follow the restriction
of a restricted-input queue (rique), in which insertions occur only at the
head, and removals occur both at the head and the tail. We characterize the
graphs admitting rique layouts with a single page and we use the
characterization to derive a corresponding testing algorithm when the input
graph is maximal planar. We finally give bounds on the number of needed pages
(so-called rique-number) of complete graphs.
