Long Cycles in 3-Connected Graphs

Moon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, then G contains a cycle of length at least Ω(nlog3 2). In this paper, this conjecture is proved. In addition, the same result is proved for 3-connected graphs embeddable in the projective plane, or the torus, or the Klein bottle.