  A graph is an opposition graph, respectively, a coalition graph, if it admits
an acyclic orientation which puts the two end-edges of every chordless 4-vertex
path in opposition, respectively, in the same direction. Opposition and
coalition graphs have been introduced and investigated in connection to perfect
graphs. Recognizing and characterizing opposition and coalition graphs are
long-standing open problems. This paper gives characterizations for opposition
graphs and coalition graphs on some restricted graph classes. Implicit in our
arguments are polynomial time recognition algorithms for these graphs. We also
give a good characterization for the so-called generalized opposition graphs.
