Clique tree generalization and new subclasses of chordal graphs (Q1348383)
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scientific article; zbMATH DE number 1742052
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Clique tree generalization and new subclasses of chordal graphs |
scientific article; zbMATH DE number 1742052 |
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Clique tree generalization and new subclasses of chordal graphs (English)
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15 May 2002
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The aim of this paper is to obtain a unique structure that reflects the interactions between the maximal cliques of a chordal graph. The authors introduce the notion of a reduced clique hypergraph of a chordal graph which generalizes the notion of a clique tree. A structure theorem which characterizes the hyperedges of the reduced clique hypergraph in terms of the minimal vertex separators is proved. Also the authors derive a formula for counting the number of clique trees of a chordal graph, and they introduce a few new subclasses of chordal graphs.
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maximal cliques
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chordal graph
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reduced clique hypergraph
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clique trees
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minimal vertex separators
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