On the Number of Cycles in 3-Connected Cubic Graphs

Letf(n) be the minimum number of cycles present in a 3-connected cubic graph onnvertices. In 1986, C. A. Barefoot, L. Clark, and R. Entringer (Congr. Numer.53, 1986) showed thatf(n) is subexponential and conjectured thatf(n) is super-polynomial. We verify this by showing that, fornsufficiently large, 2n0.17<f(n) 2n0.95.