On the number of cycles in 3-connected cubic graphs (Q1386478)
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scientific article; zbMATH DE number 1154636
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of cycles in 3-connected cubic graphs |
scientific article; zbMATH DE number 1154636 |
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On the number of cycles in 3-connected cubic graphs (English)
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10 August 1998
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Let \(f(n)\) denote the minimum number of cycles in a 3-connected cubic graph. The authors show that \(f(n)\) is superpolynomial, by showing that for \(n\) sufficiently large, \(2^{n^{0.17}}<f(n)<2^{n^{0.95}}\). This confirms a conjecture by \textit{C. A. Barefoot}, \textit{L. Clark} and \textit{R. Entringer} [Congr. Nummerantium 53, 49-62 (1986; Zbl 0623.05033)].
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number of cycles
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cubic graph
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