Convex Programming and Circumference of 3-Connected Graphs of Low Genus

The circumference of a graphGis the length of a longest cycle inG. In this paper, we shall show that, ifGis a 3-connected graph embeddable in the plane, the projective plane, the torus, or the Klein bottle, thenGhas circumference at least (1/6)×|V(G)|0.4+1. This improves a result of Jackson and Wormald.