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.

Source : oai:HAL:hal-00958979v1

Volume: Vol. 5

Published on: January 1, 2002

Submitted on: March 26, 2015

Keywords: perfect graphs.,p-connected graphs,homogeneous set,perfect graphs,Claw-free graphs,reconstruction problem,P_4-structure,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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