Recognizing the P 4-structure of claw-free graphs and a larger graph class

The P 4-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 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...

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Main Authors:	Luitpold Babel, Andreas Brandstädt, Van Bang Le
Format:	Article
Language:	English
Published:	Discrete Mathematics & Theoretical Computer Science 2002-12-01
Series:	Discrete Mathematics & Theoretical Computer Science
Online Access:	http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/171

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spelling	doaj-95516e35b4824b10b306ebe2564a9abe2020-11-25T00:02:16ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502002-12-0151Recognizing the P 4-structure of claw-free graphs and a larger graph classLuitpold BabelAndreas BrandstädtVan Bang LeThe P 4-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 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. http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/171
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Luitpold Babel Andreas Brandstädt Van Bang Le
spellingShingle	Luitpold Babel Andreas Brandstädt Van Bang Le Recognizing the P 4-structure of claw-free graphs and a larger graph class Discrete Mathematics & Theoretical Computer Science
author_facet	Luitpold Babel Andreas Brandstädt Van Bang Le
author_sort	Luitpold Babel
title	Recognizing the P 4-structure of claw-free graphs and a larger graph class
title_short	Recognizing the P 4-structure of claw-free graphs and a larger graph class
title_full	Recognizing the P 4-structure of claw-free graphs and a larger graph class
title_fullStr	Recognizing the P 4-structure of claw-free graphs and a larger graph class
title_full_unstemmed	Recognizing the P 4-structure of claw-free graphs and a larger graph class
title_sort	recognizing the p 4-structure of claw-free graphs and a larger graph class
publisher	Discrete Mathematics & Theoretical Computer Science
series	Discrete Mathematics & Theoretical Computer Science
issn	1462-7264 1365-8050
publishDate	2002-12-01
description	The P 4-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 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.
url	http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/171
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Recognizing the P 4-structure of claw-free graphs and a larger graph class

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