On weights of induced paths and cycles in claw-free and \(K_{1,r}\)-free graphs (Q2712590)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On weights of induced paths and cycles in claw-free and \(K_{1,r}\)-free graphs |
scientific article |
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8 July 2001
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claw-free graph
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induced path
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induced cycle
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degree sum
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On weights of induced paths and cycles in claw-free and \(K_{1,r}\)-free graphs (English)
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Let \(G\) be a connected \(K_{1,3}\)-free graph on \(n\) vertices, having independence number \(\alpha\). It is shown that if \(H\) is an induced path or an induced cycle having at least 6 vertices, then the sum of the degrees of vertices of \(H\) in \(G\) is less than or equal to \(4n-4\alpha\). An example is given where equality is attained. The authors generalize the result to \(K_{1,r}\)-free graphs.
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