\(P_4\)-domination in minimal imperfect graphs (Q1293209)
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scientific article; zbMATH DE number 1309397
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(P_4\)-domination in minimal imperfect graphs |
scientific article; zbMATH DE number 1309397 |
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\(P_4\)-domination in minimal imperfect graphs (English)
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4 April 2000
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A graph is said to be perfect if, for any of its induced subgraphs, the chromatic number equals the clique number. It is called minimal imperfect if it is not perfect, but all its proper induced subgraphs are. The author introduces the notion of \(P_4\)-domination and studies the relation between \(P_4\)-domination and the perfectness and graphs. Two conjectures are given. They are used to find an equivalent version of the odd pair conjecture. The author proves some particular cases of these conjectures.
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minimal imperfect graphs
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chromatic number
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clique number
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odd pair conjecture
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