Elefterie Olaru, Mihai Talmaciu:A Class of Partitionable Graphs, p.313-317

Let us call a graph

partitionable if $\theta (G)$ = $\alpha (G)$ and $\chi (G)$ = $\omega (G)$ hold. We call a graph

if there are an optimal coloring of the set of vertices of

and an optimal coloring of $\overline G$ , the complement of

, such that any color-class of

intersects any color-class of $\overline G$ . The main result of this paper is (Theorem 1): A graph

with

vertices is an O-graph iff it is partitionable and

= $\alpha (G)$ $\cdot$ $\omega (G)$ .