Discrete Mathematics & Theoretical Computer Science, Vol 5 (2002)

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DMTCS vol 5 no 1 (2002), pp. 127-146

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 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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