On the number of cycles in 3-connected cubic graphs
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)].
scientific article; zbMATH DE number 1154636