On the Number of Simple Cycles in Planar Graphs

Abstract

Let C(G) denote the number of simple cycles of a graph G and let C(n) be the maximum of C(G) over all planar graphs with n nodes. We present a lower bound on C(n), constructing graphs with at least 2.28n cycles. Applying some probabilistic arguments we prove an upper bound of 3.37n.We also discuss this question restricted to the subclasses of grid graphs, bipartite graphs, and 3-colourable triangulated graphs.