Longest cycles in 3-connected graphs Original Research Article

In this paper, we get the following result: Let G be a 3-connected graph with n vertices. Then c(G) ⩾ min{{n, σ3}}, where σ3 = min{{∑i=13 d(ui) − |∩i=13 N(ui| : {{u1, u2, u3}} is an independent set of G}}. This is a new lower bound for the circumference c(G) of a 3-connected graph G.