Long cycles in 3‐connected graphs in orientable surfaces

In this article, we apply a cutting theorem of Thomassen to show that there is a function f: N → N such that if G is a 3‐connected graph on n vertices which can be embedded in the orientable surface of genus g with face‐width at least f(g), then G contains a cycle of length at least cn, where c is a constant not dependent on g. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 69–84, 2002