# Discrete Mathematics & Theoretical Computer Science

## Volume 5 n° 1 (2002), pp. 127-146

author: | Luitpold Babel and Andreas Brandstädt and Van Bang Le |
---|---|

title: | Recognizing the P-structure of claw-free graphs and a larger graph class_{4} |

keywords: | Claw-free graphs, reconstruction problem, P-structure, _{4}p-connected graphs, homogeneous set, perfect graphs. |

abstract: | The P-structure of a graph _{4}G is a hypergraph on the same vertex set such that four vertices
form a hyperedge in H whenever they induce a
HP in _{4}G. We present a constructive algorithm
which tests in polynomial time whether a given 4-uniform hypergraph is
the P-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 _{4}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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reference: | Luitpold Babel and Andreas Brandstädt and Van Bang Le (2002),
Recognizing the P-structure of claw-free graphs and a larger graph class,
_{4}Discrete Mathematics and Theoretical Computer Science 5, pp. 127-146 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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