### Recognizing the P4-structure of claw-free graphs and a larger graph class

*Luitpold Babel, Andreas Brandstädt, Van Bang Le*

#### Abstract

The P4-structure of a graph G is a hypergraph

**H**on the same vertex set such that four vertices form a hyperedge in**H**whenever they induce a P4 in G. We present a constructive algorithm which tests in polynomial time whether a given 4-uniform hypergraph is the P4-structure of a claw-free graph and of (banner,chair,dart)-free graphs. The algorithm relies on new structural results for (banner,chair,dart)-free graphs which are based on the concept of p-connectedness. As a byproduct, we obtain a polynomial time criterion for perfectness for a large class of graphs properly containing claw-free graphs.Full Text: GZIP Compressed PostScript PostScript PDF original HTML abstract page