On strongly circular-perfectness

In this paper, we exhibit an infinite class of non rank-perfect circular-perfect graphs. We introduce strongly circular-perfectness: a circular-perfect graph is said to be strongly circular-perfect if its complement is also circular-perfect. This subclass of circular-perfect graphs includes perfect graphs, odd holes and antiholes. We show that there are infinitely many non rank-perfect strongly circular-perfect graphs and fully characterize triangle-free minimal strongly circular-imperfect graphs: it turns out that these graphs are very close to odd holes.