Even cycles in graphs with many odd cycles (Q5935601)
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scientific article; zbMATH DE number 1610695
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Even cycles in graphs with many odd cycles |
scientific article; zbMATH DE number 1610695 |
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Even cycles in graphs with many odd cycles (English)
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2 May 2002
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It is shown that if \(G\) is a graph of order \(n\) which contains a triangle, a cycle of length \(n\) or \(n-1\) and at least \(cn\) odd cycles of different lengths for some positive constant \(c\), then there exists some positive constant \(k=k(c)\) such that \(G\) contains at least \(kn^{1/6}\) even cycles of different lengths. Some related results and open problems are also presented.
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number of cycles
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even cycles
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odd cycles
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