A graph is fraternally oriented iff for every three vertices u, upsilo
n, w the existence of the edges u --> w and upsilon --> w implies that
u and v are adjacent. A directed unicyclic graph is obtained f rom a
unicyclic graph by orienting the unique cycle clockwise and by orienti
ng the appended subtrees from the cycle outwardly. Two directed subtre
es s, t of a directed unicyclic graph are proper if their union contai
ns no (directed or undirected) cycle and either they are disjoint or o
ne of them s has its root r(s) in t and contains all the successors of
r(s) in t. In the present paper we prove that G is an intersection gr
aph of a family of proper directed subtrees of a directed unicyclic gr
aph iff it has a fraternal orientation such that for every vertex upsi
lon, G(GAMMA(in)upsilon) is acyclic and G(GAMMA(out)upsilon) is the tr
ansitive closure of a tree. We describe efficient algorithms for recog
nizing when such graphs are perfect and for testing isomorphism of pro
per circular-arc graphs. (C) 1994 John Wiley & Sons, Inc.