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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2002-12-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/171 |
| Summary: | 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. |
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| ISSN: | 1462-7264 1365-8050 |