Discrete Mathematics & Theoretical Computer Science
| author: | Luitpold Babel and Andreas Brandstädt and Van Bang Le |
|---|---|
| title: | Recognizing the P4-structure of claw-free graphs and a larger graph class |
| keywords: | Claw-free graphs, reconstruction problem, P4-structure, p-connected graphs, homogeneous set, perfect graphs. |
| 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.
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| reference: | Luitpold Babel and Andreas Brandstädt and Van Bang Le (2002), Recognizing the P4-structure of claw-free graphs and a larger graph class, 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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