Let us call a graph
partitionable if
=
and
=
hold.
We call a graph
-
if there are an optimal coloring of the set
of vertices of
and an optimal coloring of
, the complement of
, such that
any color-class of
intersects any color-class of
. The main result of
this paper is (Theorem 1): A graph
with
vertices is an O-graph iff it is
partitionable and
=
.