Circumference of 3-connected cubic graphs

The circumference of a graph is the length of its longest cycles. Jackson established a conjecture of Bondy by showing that the circumference of a 3-connected cubic graph of order n is Ω(n0.694). Bilinski et al. improved this lower bound to Ω(n0.753) by studying large Eulerian subgraphs in 3-edge-connected graphs. In this paper, we further improve this lower bound to Ω(n0.8). This is done by considering certain 2-connected cubic graphs, finding cycles through two given edges, and distinguishing the cases according to whether or not these edges are adjacent.