Oriented expressions of graph properties

Several graph properties are characterized as a class of graphs that admit an orientation avoiding finite set oriented structures. For instance, if Fk is the homomorphic images directed path on k+1 vertices, then k-colourable and only it admits with no induced subgraph in Fk. There fundamental question underlying this kind characterizations: Given property P, there F such belongs to P F? We address by exhibiting some necessary conditions upon certain classes for them characterization. Consequently, we exhibit uncountable family hereditary which exists. In particular, holes prime length family.