more generally, a graph "g" is said to be a line perfect graph if "l"("g") is a perfect graph. the line perfect graphs are exactly the graphs that do not contain a simple cycle of odd length greater than three. equivalently, a graph is line perfect if and only if each of its biconnected components is either bipartite or of the form "k" (the tetrahedron) or "k" (a book of one or more triangles all sharing a common edge). every line perfect graph is itself perfect.