关于路图P_k(G)的一点注记

A Note on the Path Graph P_k(G)

本文主要得到结论：图Ｐ３（Ｇ） 是完美图的充要条件是图Ｇ不含有长至少为５ 的奇圈和图Ｈ 作为子图；２－连通图Ｇ的路图Ｐ３（Ｇ）是２－连通图；以及ｘ（Ｐ３（ｋｎ））≤４，当ｎ≤９时等．

In this paper, 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.