w egetthefollow ing m ain results:the graph P3(G)is perfectifand only ifthe graph Gdoes notcontain a cycle ofodd length atleastfiveand the graph H as its subgraphs; the path graph P3(G)ofa 2- connected graph Gis 2-connected
and the chrom atic num ber ofthe path graph P3(Κn)(n ≤9) is notlarge than four etc.