P 4-Isomorphic graphs

[math]\displaystyle{ P_{4} }[/math]-Isomorphic graphs --- [math]\displaystyle{ P_{4} }[/math]-изоморфные графы.

The graphs [math]\displaystyle{ G_{1} = (V, E_{1}) }[/math] and [math]\displaystyle{ G_{2} = (V, E_{2}) }[/math] with the same vertex set [math]\displaystyle{ V }[/math] are [math]\displaystyle{ P_{4} }[/math]-isomorphic graphs if for any set [math]\displaystyle{ S \subseteq V }[/math] of 4 vertices it holds that [math]\displaystyle{ S }[/math] induces [math]\displaystyle{ P_{4} }[/math] in [math]\displaystyle{ G_{1} }[/math] iff [math]\displaystyle{ S }[/math] induces [math]\displaystyle{ P_{4} }[/math] in [math]\displaystyle{ G_{2} }[/math].

In 1984, V.Chvatal conjectured that if a graph is [math]\displaystyle{ P_{4} }[/math]-isomorphic to a perfect graph, then it is perfect. This conjecture is known as Semi-Strong Perfect Graph Conjecture. In 1987, B.Reed showed that this conjecture is true.