Tree-decompositions, tree-representability and chordal graphs (Q1104938)
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scientific article; zbMATH DE number 4057559
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tree-decompositions, tree-representability and chordal graphs |
scientific article; zbMATH DE number 4057559 |
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Tree-decompositions, tree-representability and chordal graphs (English)
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1988
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The following assertions are shown to be equivalent, for any countable graph G: (1) G can be represented as the intersection graph of a family of subtrees of a tree; (2) G admits a tree-decomposition (Robertson/Seymour) into primes; (3) G is chordal, and G admits a simplicial tree-decomposition (Halin) into primes; (4) G is chordal, and neither of two specified graphs is contained in G as a simplicial minor.
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intersection graph
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tree-decomposition
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chordal
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simplicial minor
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