On the König graphs for a 5-path and its spanning supergraphs

We describe the hereditary class of graphs whose every subgraph has the property that the maximum number of disjoint 5-paths (paths on 5 vertices) is equal to the minimum size of the sets of vertices having nonempty intersection with the vertex set of each 5-path. We describe this class in terms of the “forbidden subgraphs” and give an alternative description, using some operations on pseudographs. Illustr. 2, bibliogr. 18.