Berge graphs with chordless cycles of bounded length

A graph is called weakly triangulated if it contains no chordless cycle on ve or more vertices (also called hole) and no complement of such a cycle (also called antihole). Equivalently, we can deene weakly triangulated graphs as antihole-free graphs whose induced cycles are isomorphic either to C3 or to C4. The perfection of weakly triangulated graphs was proved by Hayward 3] and generated intense studies to eeciently solve, for these graphs,the classical NP-complete problems which become polynomial on perfect graphs. If we replace, in the deenition above, the C4 by an arbitrary Cp (p even, at least equal to 6), we obtain new classes of graphs whose perfection is shown in this paper. In fact, we prove a more general result: for any even integer p 6, the graphs whose cycles are isomorphic either to C3 or to one of