On the number of cycles of length k in a maximal planar graph
S. L. Hakimi, Edward F. Schmeichel · Journal of Graph Theory · 1979
Abstract Let G be a maximal planar graph with p vertices, and let Ck(G) denote the number of cycles of length k in G. We first present tight bounds for C3(G) and C4(G) in terms of p. We then give bounds for Ck(G) when 5 ≤ k ≤ p, and consider in particular bounds for Cp(G), in terms of p. Some conjectures and unsolved problems are stated.