Slightly triangulated graphs are perfect (Q1340126)
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scientific article; zbMATH DE number 700942
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Slightly triangulated graphs are perfect |
scientific article; zbMATH DE number 700942 |
Statements
Slightly triangulated graphs are perfect (English)
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9 February 1995
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A graph \(G\) is said to be slightly triangulated iff \(G\) has the following two properties: (i) \(G\) contains no chordless cycle with at least 5 vertices, and (ii) for every induced subgraph \(H\) of \(G\), there is a vertex in \(H\) the neighbourhood of which in \(H\) contains no chordless path of 4 vertices. The author shows that every slightly triangulated graph is perfect. Comparisons with other classes of perfect graphs and open problems are considered too.
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chordless cycle
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chordless path
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slightly triangulated graph
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perfect graphs
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