Recognizing the P4-structure of block graphs

A 4-uniform hypergraph represents the P4-structure of a graph G, if its hyperedges are the vertex sets of the induced paths P4 in G. We shall give in this paper a simple algorithm that recognizes the P4-structure of a block graph in polynomial time. Here, block graphs are connected graphs in which all maximal 2-connected subgraphs are cliques. Our algorithm is based on a similar approach as that for trees by the authors and S. Olariu using weighted 2-section graphs of hypergraphs.