These P₄-free graphs are also known as co-graphs. A simple proof of the perfectness of such graphs was given by Seinsche, On a property of the class of n-colorable graphs, J. Comb. Th. Ser. B 16 (1974), 191–193. MR0337679 The key to the proof is the fact that these graphs are also characterized by the property that every subset of $V(G)$ with more than one element is either not $G$-connected or not $\overline{G}$-connected. It follows that every such graph can be obtained from a single vertex by repeatedly duplicating vertices with or without an edge between the two duplicates. Since these two duplication operations preserve perfectness, all such graphs are perfect. (This quick argument is due to Lovász.)

These P₄-free graphs are also known as cographs. A simple proof of the perfectness of such graphs was given by Seinsche, On a property of the class of n-colorable graphs, J. Comb. Th. Ser. B 16 (1974), 191–193. MR0337679 The key to the proof is the fact that these graphs are also characterized by the property that every subset of $V(G)$ with more than one element is either not $G$-connected or not $\overline{G}$-connected. It follows that every such graph can be obtained from a single vertex by repeatedly duplicating vertices with or without an edge between the two duplicates. Since these two duplication operations preserve perfectness, all such graphs are perfect. (This quick argument is due to Lovász.)

These P₄-free graphs are also known as co-graphs. A simple proof of the perfectness of such graphs was given by Seinsche, On a property of the class of n-colorable graphs, J. Comb. Th. Ser. B 16 (1974), 191–193. MR0337679 The key to the proof is the fact that these graphs are also characterized by the property that every subset of $V(G)$ with more than one element is either not $G$-connected or not $\overline{G}$-connected.

These P₄-free graphs are also known as co-graphs. A simple proof of the perfectness of such graphs was given by Seinsche, On a property of the class of n-colorable graphs, J. Comb. Th. Ser. B 16 (1974), 191–193. MR0337679 The key to the proof is the fact that these graphs are also characterized by the property that every subset of $V(G)$ with more than one element is either not $G$-connected or not $\overline{G}$-connected. It follows that every such graph can be obtained from a single vertex by repeatedly duplicating vertices with or without an edge between the two duplicates. Since these two duplication operations preserve perfectness, all such graphs are perfect. (This quick argument is due to Lovász.)