Weak clique-covering cycles and paths. (Q2716000)
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scientific article; zbMATH DE number 1600969
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak clique-covering cycles and paths. |
scientific article; zbMATH DE number 1600969 |
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20 July 2005
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longest cycle
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degree condition
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neighborhood union condition
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Weak clique-covering cycles and paths. (English)
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A cycle \(C\) of a graph \(G\) is said to be a covering cycle, or briefly \(C\)-cycle, if \(V(G)-V(C)\) is an independent set. A cycle \(C\) is a weak clique-covering cycle, or \(CC\)-cycle of \(G\), if each component of \(G-V(C)\) is a clique. Clearly, every \(C\)-cycle is also a \(CC\)-cycle. The concepts of a \(C\)-path and \(CC\)-path are defined analogously. The results of the paper give several degree conditions and neighborhood union conditions for a graph to have a \(CC\)-cycle or to have a \(CC\)-path with given endvertices.
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