  Path graphs are intersection graphs of paths in a tree. We start from the
characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei,
Intersection Graphs of Paths in a Tree, J. Combin. Theory Ser. B, 41:2 (1986)
141--181] and we reduce it to some 2-colorings subproblems, obtaining the first
characterization that directly leads to a polynomial recognition algorithm.
Then we introduce the collection of the attachedness graphs of a graph and we
exhibit a list of minimal forbidden 2-edge colored subgraphs in each of the
attachedness graph.
