Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap CoNP$ without resorting to existing polynomial time algorithms. The characterization is given in terms of the collection of the \emph{attachedness graphs} of a graph, a novel device to deal with the connected components of a graph after the removal of clique separators. On the one hand, the characterization refines and simplifies the characterization of path graphs due to Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection {G}raphs of {P}aths in a {T}ree, J. Combin. Theory Ser. B, 41:2 (1986) 141--181], which we build on, by reducing a constrained vertex coloring problem defined on the \emph{attachedness graphs} to a vertex 2-coloring problem on the same graphs. On the other hand, the characterization allows us to exhibit two exhaustive lists of obstructions to path graph membership in the form of minimal forbidden induced/partial 2-edge colored subgraphs in each of the \emph{attachedness graphs}.

翻译：路径图是树中路径的交叉图。 ~ 在本文中, 我们给出路径图的“ 6\ 良好定性”, 也就是说, 我们证明路径图成员为$NP\ cap CoNP$, 而不用利用现有的多元时间算法 。 属性的描述是以图表 {T} 的 emph{ attatecendies 图形的收集方式表示的。 图表是一个新颖的设备, 用于处理删除 cluique 分隔器之后的图形的连接组件 。 一方面, 描述精细化和简化因 Monma 和 Wei 而导致的路径图的定性 。 [C. L. ~ Monma, ~ ~ ~ ~ ~ ~ K. Wei, Intersection {G} raphs {P} 在 {T}reme, J. 组合。 Theory Ser. B, 41: 2 (1986) 141- 181), 我们通过减少在 emph { attendness 图表中定义的受限制的垂直颜色图表问题来定义的精化问题 和简化图中, 的图中, 的图面图面图表2色色色图的图的图的图, 使我们可以建立相同的图的图。