On a closure concept in claw-free graphs (Q1362093)
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scientific article; zbMATH DE number 1042495
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a closure concept in claw-free graphs |
scientific article; zbMATH DE number 1042495 |
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On a closure concept in claw-free graphs (English)
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12 August 1997
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If \(G\) is a claw-free graph, then there is a graph \(cl(G)\) such that (i) \(G\) is a spanning subgraph of \(cl(G)\), (ii) \(cl(G)\) is a line graph of a triangle-free graph, and (iii) the length of a longest cycle in \(G\) and in \(cl(G)\) is the same. A sufficient condition for hamiltonicity in claw-free graphs, the equivalence of some conjectures on hamiltonicity in 2-tough graphs and the hamiltonicity of 7-connected claw-free graphs are obtained as corollaries.
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claw-free graph
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hamiltonicity
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