  Min orderings give a vertex ordering characterization, common to some graphs
and digraphs such as interval graphs, complements of threshold tolerance graphs
(known as co-TT graphs), and two-directional orthogonal ray graphs. An adjusted
interval digraph is a reflexive digraph that has a min ordering. Adjusted
interval digraph can be recognized in $O(n^4)$ time, where $n$ is the number of
vertices of the given graph. Finding a more efficient algorithm is posed as an
open question. This note provides a new recognition algorithm with running time
$O(n^3)$. The algorithm produces a min ordering if the given graph is an
adjusted interval digraph.
