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Recognizing the P_4-structure of claw-free graphs and a larger graph class

Abstract : 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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Luitpold Babel, Andreas Brandstädt, van Bang Le. Recognizing the P_4-structure of claw-free graphs and a larger graph class. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2002, Vol. 5, pp.127-146. ⟨10.46298/dmtcs.294⟩. ⟨hal-00958979⟩

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