Geodesic
Recognizing the P_4-structure of claw-free graphs and a larger graph class
Discrete mathematics & theoretical computer science, Tome 5 (2002).

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The P_4-structure of a graph G is a hypergraph \textbfH on the same vertex set such that four vertices form a hyperedge in \textbfH whenever they induce a P_4 in G. We present a constructive algorithm which tests in polynomial time whether a given 4-uniform hypergraph is the P_4-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. 
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     author = {Babel, Luitpold and Brandst\"adt, Andreas and Le, Van Bang},
     title = {Recognizing the {P_4-structure} of claw-free graphs and a larger graph class},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {5},
     year = {2002},
     doi = {10.46298/dmtcs.294},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.294/}
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Babel, Luitpold; Brandstädt, Andreas; Le, Van Bang. Recognizing the P_4-structure of claw-free graphs and a larger graph class. Discrete mathematics & theoretical computer science, Tome 5 (2002). doi : 10.46298/dmtcs.294. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.294/

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